Name: Unit 3: Relations and Functions Date: Per Homework 5: Zeros of Functions Directions: Identify the zeros of the function given the graph 1. 2. 3 6. Directions: Identify the zeros of the function algebraically 7. () = 1+2 8. S(x) = -2x+6 10. \/) – 2x – 10 11.\/6–**** 12. (:) – 4 Directions: Identify the zeros of the function using your graphing colculator 13. f(x) = -2 14. () = -2x-15 15. () — 5x + 6 16. \/() – x – 6x + 3x +10 17. () = x-2x-x+2 18. (*) -x-5x20x-16<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n Let’s break down how to identify the zeros of functions given various forms (graphical, algebraic, and using a graphing calculator). The zeros of a function are the points where the function’s output is equal to zero (i.e., ( f(x) = 0 )).<\/p>\n\n\n\n If you have a graph of the function, you can identify the zeros by looking for the points where the graph crosses the x-axis. These are the points where the value of ( f(x) = 0 ). The x-coordinates of these points are the zeros of the function. If the graph does not cross the x-axis, there are no real zeros. If the graph touches the x-axis at a single point or multiple points, those are the zeros.<\/p>\n\n\n\n Here\u2019s how to find the zeros for the functions provided:<\/p>\n\n\n\n To find the zeros of ( f(x) = x + 2 ), set ( f(x) = 0 ) and solve for ( x ): To find the zeros of ( S(x) = -2x + 6 ), set ( S(x) = 0 ) and solve for ( x ): To find the zeros of ( f(x) = -2x – 10 ), set ( f(x) = 0 ) and solve for ( x ): To find the zeros of ( f(x) = 6x – 10 ), set ( f(x) = 0 ) and solve for ( x ): Since the function is a constant, it never crosses the x-axis. Therefore, this function has no zeros<\/strong>.<\/p>\n\n\n\n For functions like:<\/p>\n\n\n\n You would input these functions into your graphing calculator and identify where they intersect the x-axis (or if they do not).<\/p>\n\n\n\n For example, with ( f(x) = -2x – 15 ), you set the equation equal to zero, solve for ( x ), and graph the function. The graph crosses the x-axis at ( x = -\\frac{15}{2} ).<\/p>\n\n\n\n Similarly, for the cubic equation, you would find the zeros by factoring or using the calculator\u2019s graphing tool to locate the points where the curve intersects the x-axis.<\/p>\n\n\n\n The zeros of a function represent the points where the function equals zero. You can find these algebraically by setting the function equal to zero and solving for ( x ). When using a graphing calculator, the zeros are the x-intercepts of the function’s graph. Functions such as constants (e.g., ( f(x) = -4 )) may have no zeros, while linear functions (e.g., ( f(x) = x + 2 )) will always have exactly one zero.<\/p>\n","protected":false},"excerpt":{"rendered":" Name: Unit 3: Relations and Functions Date: Per Homework 5: Zeros of Functions Directions: Identify the zeros of the function given the graph 1. 2. 3 6. Directions: Identify the zeros of the function algebraically 7. () = 1+2 8. S(x) = -2x+6 10. \/) – 2x – 10 11.\/6–**** 12. (:) – 4 Directions: […]<\/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-188688","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188688","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=188688"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188688\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188688"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188688"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188688"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Part 1: Identifying Zeros from a Graph<\/h3>\n\n\n\n
Part 2: Identifying Zeros Algebraically<\/h3>\n\n\n\n
7. ( f(x) = x + 2 )<\/h4>\n\n\n\n
[
x + 2 = 0
]
[
x = -2
]
So, the zero of the function is ( x = -2 ).<\/p>\n\n\n\n8. ( S(x) = -2x + 6 )<\/h4>\n\n\n\n
[
-2x + 6 = 0
]
[
-2x = -6
]
[
x = 3
]
So, the zero of the function is ( x = 3 ).<\/p>\n\n\n\n10. ( f(x) = -2x – 10 )<\/h4>\n\n\n\n
[
-2x – 10 = 0
]
[
-2x = 10
]
[
x = -5
]
So, the zero of the function is ( x = -5 ).<\/p>\n\n\n\n11. ( f(x) = 6x – 10 )<\/h4>\n\n\n\n
[
6x – 10 = 0
]
[
6x = 10
]
[
x = \\frac{10}{6} = \\frac{5}{3}
]
So, the zero of the function is ( x = \\frac{5}{3} ).<\/p>\n\n\n\n12. ( f(x) = -4 )<\/h4>\n\n\n\n
Part 3: Identifying Zeros Using a Graphing Calculator<\/h3>\n\n\n\n
\n
Conclusion<\/h3>\n\n\n\n