\n\n\n\n
Given Piecewise Function:<\/strong><\/h3>\n\n\n\nH(x)={x2\u221216x\u22124,if x\u226047,if x=4H(x) = \\begin{cases} \\frac{x^2 – 16}{x – 4}, & \\text{if } x \\ne 4 \\\\ 7, & \\text{if } x = 4 \\end{cases}<\/p>\n\n\n\n
We are asked to find:<\/p>\n\n\n\n
\n- (A) H(3)H(3)<\/li>\n\n\n\n
- (B) H(0)H(0)<\/li>\n\n\n\n
- (C) H(4)H(4)<\/li>\n\n\n\n
- Domain<\/li>\n\n\n\n
- Graph the function<\/li>\n\n\n\n
- Use the graph to find the range<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\u2705 Step-by-Step Evaluations:<\/h2>\n\n\n\n
\n\n\n\n(A) H(3)H(3)<\/strong><\/h3>\n\n\n\nSince x=3\u22604x = 3 \\ne 4, use: H(x)=x2\u221216x\u22124H(x) = \\frac{x^2 – 16}{x – 4} H(3)=32\u2212163\u22124=9\u221216\u22121=\u22127\u22121=7H(3) = \\frac{3^2 – 16}{3 – 4} = \\frac{9 – 16}{-1} = \\frac{-7}{-1} = 7<\/p>\n\n\n\n
\n\n\n\n(B) H(0)H(0)<\/strong><\/h3>\n\n\n\nSince x=0\u22604x = 0 \\ne 4, use the same expression: H(0)=02\u2212160\u22124=\u221216\u22124=4H(0) = \\frac{0^2 – 16}{0 – 4} = \\frac{-16}{-4} = 4<\/p>\n\n\n\n
\n\n\n\n(C) H(4)H(4)<\/strong><\/h3>\n\n\n\nSince x=4x = 4, we use the second part of the function: H(4)=7H(4) = 7<\/p>\n\n\n\n
\n\n\n\n\u2705 Final Answers:<\/h2>\n\n\n\n\n- (A) H(3)=7H(3) = 7<\/li>\n\n\n\n
- (B) H(0)=4H(0) = 4<\/li>\n\n\n\n
- (C) H(4)=7H(4) = 7<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83c\udf10 Domain of H(x)H(x):<\/h2>\n\n\n\n
The function is defined for all real numbers<\/strong>, including x=4x = 4, because it assigns a separate value at that point.<\/p>\n\n\n\n\nSo the domain is:<\/p>\n<\/blockquote>\n\n\n\n
(\u2212\u221e,\u221e)\\boxed{(-\\infty, \\infty)}<\/p>\n\n\n\n
\n\n\n\n\ud83d\udcc9 Graph and Explanation:<\/h2>\n\n\n\n
To graph the function, consider the simplified form of the first part. x2\u221216x\u22124=(x\u22124)(x+4)x\u22124=x+4,for x\u22604\\frac{x^2 – 16}{x – 4} = \\frac{(x – 4)(x + 4)}{x – 4} = x + 4, \\quad \\text{for } x \\ne 4<\/p>\n\n\n\n
So the graph is:<\/p>\n\n\n\n
\n- A line<\/strong> y=x+4y = x + 4, with a hole at<\/strong> x=4x = 4<\/li>\n\n\n\n
- At x=4x = 4, the function jumps to y=7y = 7<\/strong><\/li>\n<\/ul>\n\n\n\n
This is a piecewise discontinuous function:<\/p>\n\n\n\n
\n- A straight line with a hole<\/strong> at (4,8)(4, 8)<\/li>\n\n\n\n
- A filled dot<\/strong> at (4,7)(4, 7)<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83d\udcca Range of H(x)H(x):<\/h2>\n\n\n\n
The line y=x+4y = x + 4 covers all real numbers except<\/strong> at x=4x = 4, where it jumps from y=8y = 8 to y=7y = 7.<\/p>\n\n\n\nSo the output at x=4x = 4 is 7<\/strong>, but y=8y = 8 is never taken<\/strong> because of the hole.<\/p>\n\n\n\n\nThe range<\/strong> is:<\/p>\n<\/blockquote>\n\n\n\n(\u2212\u221e,8)\u222a{7}\u222a(8,\u221e)\\boxed{(-\\infty, 8) \\cup \\{7\\} \\cup (8, \\infty)}<\/p>\n\n\n\n
We include 7 because H(4)=7H(4) = 7, but exclude 8 because the function never equals 8.<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/learnexams-banner7-88.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"Evaluate The Piecewise Function At The Given Values Of The Independent Variable. If X #4 X\u00b2 \u2013 16 H(X) = {X-4 7 If X = 4 (A) H(3) (B) H(0) (C) H(4) (A) H(3)= (B) H(0) = (C) H(4)=1 The Domain Of The Piecewise Function Is ( -00,00) A. Graph The Function B. Use Your […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-221084","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=221084"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=221084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=221084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=221084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n
\u2705 Step-by-Step Evaluations:<\/h2>\n\n\n\n
\n\n\n\n(A) H(3)H(3)<\/strong><\/h3>\n\n\n\nSince x=3\u22604x = 3 \\ne 4, use: H(x)=x2\u221216x\u22124H(x) = \\frac{x^2 – 16}{x – 4} H(3)=32\u2212163\u22124=9\u221216\u22121=\u22127\u22121=7H(3) = \\frac{3^2 – 16}{3 – 4} = \\frac{9 – 16}{-1} = \\frac{-7}{-1} = 7<\/p>\n\n\n\n
\n\n\n\n(B) H(0)H(0)<\/strong><\/h3>\n\n\n\nSince x=0\u22604x = 0 \\ne 4, use the same expression: H(0)=02\u2212160\u22124=\u221216\u22124=4H(0) = \\frac{0^2 – 16}{0 – 4} = \\frac{-16}{-4} = 4<\/p>\n\n\n\n
\n\n\n\n(C) H(4)H(4)<\/strong><\/h3>\n\n\n\nSince x=4x = 4, we use the second part of the function: H(4)=7H(4) = 7<\/p>\n\n\n\n
\n\n\n\n\u2705 Final Answers:<\/h2>\n\n\n\n\n- (A) H(3)=7H(3) = 7<\/li>\n\n\n\n
- (B) H(0)=4H(0) = 4<\/li>\n\n\n\n
- (C) H(4)=7H(4) = 7<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83c\udf10 Domain of H(x)H(x):<\/h2>\n\n\n\n
The function is defined for all real numbers<\/strong>, including x=4x = 4, because it assigns a separate value at that point.<\/p>\n\n\n\n\nSo the domain is:<\/p>\n<\/blockquote>\n\n\n\n
(\u2212\u221e,\u221e)\\boxed{(-\\infty, \\infty)}<\/p>\n\n\n\n
\n\n\n\n\ud83d\udcc9 Graph and Explanation:<\/h2>\n\n\n\n
To graph the function, consider the simplified form of the first part. x2\u221216x\u22124=(x\u22124)(x+4)x\u22124=x+4,for x\u22604\\frac{x^2 – 16}{x – 4} = \\frac{(x – 4)(x + 4)}{x – 4} = x + 4, \\quad \\text{for } x \\ne 4<\/p>\n\n\n\n
So the graph is:<\/p>\n\n\n\n
\n- A line<\/strong> y=x+4y = x + 4, with a hole at<\/strong> x=4x = 4<\/li>\n\n\n\n
- At x=4x = 4, the function jumps to y=7y = 7<\/strong><\/li>\n<\/ul>\n\n\n\n
This is a piecewise discontinuous function:<\/p>\n\n\n\n
\n- A straight line with a hole<\/strong> at (4,8)(4, 8)<\/li>\n\n\n\n
- A filled dot<\/strong> at (4,7)(4, 7)<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83d\udcca Range of H(x)H(x):<\/h2>\n\n\n\n
The line y=x+4y = x + 4 covers all real numbers except<\/strong> at x=4x = 4, where it jumps from y=8y = 8 to y=7y = 7.<\/p>\n\n\n\nSo the output at x=4x = 4 is 7<\/strong>, but y=8y = 8 is never taken<\/strong> because of the hole.<\/p>\n\n\n\n\nThe range<\/strong> is:<\/p>\n<\/blockquote>\n\n\n\n(\u2212\u221e,8)\u222a{7}\u222a(8,\u221e)\\boxed{(-\\infty, 8) \\cup \\{7\\} \\cup (8, \\infty)}<\/p>\n\n\n\n
We include 7 because H(4)=7H(4) = 7, but exclude 8 because the function never equals 8.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Evaluate The Piecewise Function At The Given Values Of The Independent Variable. If X #4 X\u00b2 \u2013 16 H(X) = {X-4 7 If X = 4 (A) H(3) (B) H(0) (C) H(4) (A) H(3)= (B) H(0) = (C) H(4)=1 The Domain Of The Piecewise Function Is ( -00,00) A. Graph The Function B. Use Your […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-221084","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=221084"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=221084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=221084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=221084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Since x=3\u22604x = 3 \\ne 4, use: H(x)=x2\u221216x\u22124H(x) = \\frac{x^2 – 16}{x – 4} H(3)=32\u2212163\u22124=9\u221216\u22121=\u22127\u22121=7H(3) = \\frac{3^2 – 16}{3 – 4} = \\frac{9 – 16}{-1} = \\frac{-7}{-1} = 7<\/p>\n\n\n\n
\n\n\n\n
(B) H(0)H(0)<\/strong><\/h3>\n\n\n\nSince x=0\u22604x = 0 \\ne 4, use the same expression: H(0)=02\u2212160\u22124=\u221216\u22124=4H(0) = \\frac{0^2 – 16}{0 – 4} = \\frac{-16}{-4} = 4<\/p>\n\n\n\n
\n\n\n\n(C) H(4)H(4)<\/strong><\/h3>\n\n\n\nSince x=4x = 4, we use the second part of the function: H(4)=7H(4) = 7<\/p>\n\n\n\n
\n\n\n\n\u2705 Final Answers:<\/h2>\n\n\n\n\n- (A) H(3)=7H(3) = 7<\/li>\n\n\n\n
- (B) H(0)=4H(0) = 4<\/li>\n\n\n\n
- (C) H(4)=7H(4) = 7<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83c\udf10 Domain of H(x)H(x):<\/h2>\n\n\n\n
The function is defined for all real numbers<\/strong>, including x=4x = 4, because it assigns a separate value at that point.<\/p>\n\n\n\n\nSo the domain is:<\/p>\n<\/blockquote>\n\n\n\n
(\u2212\u221e,\u221e)\\boxed{(-\\infty, \\infty)}<\/p>\n\n\n\n
\n\n\n\n\ud83d\udcc9 Graph and Explanation:<\/h2>\n\n\n\n
To graph the function, consider the simplified form of the first part. x2\u221216x\u22124=(x\u22124)(x+4)x\u22124=x+4,for x\u22604\\frac{x^2 – 16}{x – 4} = \\frac{(x – 4)(x + 4)}{x – 4} = x + 4, \\quad \\text{for } x \\ne 4<\/p>\n\n\n\n
So the graph is:<\/p>\n\n\n\n
\n- A line<\/strong> y=x+4y = x + 4, with a hole at<\/strong> x=4x = 4<\/li>\n\n\n\n
- At x=4x = 4, the function jumps to y=7y = 7<\/strong><\/li>\n<\/ul>\n\n\n\n
This is a piecewise discontinuous function:<\/p>\n\n\n\n
\n- A straight line with a hole<\/strong> at (4,8)(4, 8)<\/li>\n\n\n\n
- A filled dot<\/strong> at (4,7)(4, 7)<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83d\udcca Range of H(x)H(x):<\/h2>\n\n\n\n
The line y=x+4y = x + 4 covers all real numbers except<\/strong> at x=4x = 4, where it jumps from y=8y = 8 to y=7y = 7.<\/p>\n\n\n\nSo the output at x=4x = 4 is 7<\/strong>, but y=8y = 8 is never taken<\/strong> because of the hole.<\/p>\n\n\n\n\nThe range<\/strong> is:<\/p>\n<\/blockquote>\n\n\n\n(\u2212\u221e,8)\u222a{7}\u222a(8,\u221e)\\boxed{(-\\infty, 8) \\cup \\{7\\} \\cup (8, \\infty)}<\/p>\n\n\n\n
We include 7 because H(4)=7H(4) = 7, but exclude 8 because the function never equals 8.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Evaluate The Piecewise Function At The Given Values Of The Independent Variable. If X #4 X\u00b2 \u2013 16 H(X) = {X-4 7 If X = 4 (A) H(3) (B) H(0) (C) H(4) (A) H(3)= (B) H(0) = (C) H(4)=1 The Domain Of The Piecewise Function Is ( -00,00) A. Graph The Function B. Use Your […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-221084","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=221084"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=221084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=221084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=221084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Since x=4x = 4, we use the second part of the function: H(4)=7H(4) = 7<\/p>\n\n\n\n
\n\n\n\n
\u2705 Final Answers:<\/h2>\n\n\n\n\n- (A) H(3)=7H(3) = 7<\/li>\n\n\n\n
- (B) H(0)=4H(0) = 4<\/li>\n\n\n\n
- (C) H(4)=7H(4) = 7<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83c\udf10 Domain of H(x)H(x):<\/h2>\n\n\n\n
The function is defined for all real numbers<\/strong>, including x=4x = 4, because it assigns a separate value at that point.<\/p>\n\n\n\n\nSo the domain is:<\/p>\n<\/blockquote>\n\n\n\n
(\u2212\u221e,\u221e)\\boxed{(-\\infty, \\infty)}<\/p>\n\n\n\n
\n\n\n\n\ud83d\udcc9 Graph and Explanation:<\/h2>\n\n\n\n
To graph the function, consider the simplified form of the first part. x2\u221216x\u22124=(x\u22124)(x+4)x\u22124=x+4,for x\u22604\\frac{x^2 – 16}{x – 4} = \\frac{(x – 4)(x + 4)}{x – 4} = x + 4, \\quad \\text{for } x \\ne 4<\/p>\n\n\n\n
So the graph is:<\/p>\n\n\n\n
\n- A line<\/strong> y=x+4y = x + 4, with a hole at<\/strong> x=4x = 4<\/li>\n\n\n\n
- At x=4x = 4, the function jumps to y=7y = 7<\/strong><\/li>\n<\/ul>\n\n\n\n
This is a piecewise discontinuous function:<\/p>\n\n\n\n
\n- A straight line with a hole<\/strong> at (4,8)(4, 8)<\/li>\n\n\n\n
- A filled dot<\/strong> at (4,7)(4, 7)<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83d\udcca Range of H(x)H(x):<\/h2>\n\n\n\n
The line y=x+4y = x + 4 covers all real numbers except<\/strong> at x=4x = 4, where it jumps from y=8y = 8 to y=7y = 7.<\/p>\n\n\n\nSo the output at x=4x = 4 is 7<\/strong>, but y=8y = 8 is never taken<\/strong> because of the hole.<\/p>\n\n\n\n\nThe range<\/strong> is:<\/p>\n<\/blockquote>\n\n\n\n(\u2212\u221e,8)\u222a{7}\u222a(8,\u221e)\\boxed{(-\\infty, 8) \\cup \\{7\\} \\cup (8, \\infty)}<\/p>\n\n\n\n
We include 7 because H(4)=7H(4) = 7, but exclude 8 because the function never equals 8.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Evaluate The Piecewise Function At The Given Values Of The Independent Variable. If X #4 X\u00b2 \u2013 16 H(X) = {X-4 7 If X = 4 (A) H(3) (B) H(0) (C) H(4) (A) H(3)= (B) H(0) = (C) H(4)=1 The Domain Of The Piecewise Function Is ( -00,00) A. Graph The Function B. Use Your […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-221084","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=221084"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=221084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=221084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=221084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n
\ud83c\udf10 Domain of H(x)H(x):<\/h2>\n\n\n\n
The function is defined for all real numbers<\/strong>, including x=4x = 4, because it assigns a separate value at that point.<\/p>\n\n\n\n So the domain is:<\/p>\n<\/blockquote>\n\n\n\n (\u2212\u221e,\u221e)\\boxed{(-\\infty, \\infty)}<\/p>\n\n\n\n To graph the function, consider the simplified form of the first part. x2\u221216x\u22124=(x\u22124)(x+4)x\u22124=x+4,for x\u22604\\frac{x^2 – 16}{x – 4} = \\frac{(x – 4)(x + 4)}{x – 4} = x + 4, \\quad \\text{for } x \\ne 4<\/p>\n\n\n\n So the graph is:<\/p>\n\n\n\n This is a piecewise discontinuous function:<\/p>\n\n\n\n The line y=x+4y = x + 4 covers all real numbers except<\/strong> at x=4x = 4, where it jumps from y=8y = 8 to y=7y = 7.<\/p>\n\n\n\n So the output at x=4x = 4 is 7<\/strong>, but y=8y = 8 is never taken<\/strong> because of the hole.<\/p>\n\n\n\n The range<\/strong> is:<\/p>\n<\/blockquote>\n\n\n\n (\u2212\u221e,8)\u222a{7}\u222a(8,\u221e)\\boxed{(-\\infty, 8) \\cup \\{7\\} \\cup (8, \\infty)}<\/p>\n\n\n\n We include 7 because H(4)=7H(4) = 7, but exclude 8 because the function never equals 8.<\/p>\n\n\n\n Evaluate The Piecewise Function At The Given Values Of The Independent Variable. If X #4 X\u00b2 \u2013 16 H(X) = {X-4 7 If X = 4 (A) H(3) (B) H(0) (C) H(4) (A) H(3)= (B) H(0) = (C) H(4)=1 The Domain Of The Piecewise Function Is ( -00,00) A. Graph The Function B. Use Your […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-221084","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=221084"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221084\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=221084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=221084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=221084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\n\n\n\n\ud83d\udcc9 Graph and Explanation:<\/h2>\n\n\n\n
\n
\n
\n\n\n\n\ud83d\udcca Range of H(x)H(x):<\/h2>\n\n\n\n
\n
<\/figure>\n","protected":false},"excerpt":{"rendered":"