{"id":227163,"date":"2025-06-06T02:46:24","date_gmt":"2025-06-06T02:46:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227163"},"modified":"2025-06-06T02:46:26","modified_gmt":"2025-06-06T02:46:26","slug":"which-function-is-graphed-below-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/which-function-is-graphed-below-2\/","title":{"rendered":"Which function is graphed below"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Which function is graphed below<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The graph shown represents the function: f(x)=1xf(x) = \\frac{1}{x}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The graph provided is a classic representation of a <strong>reciprocal function<\/strong>, which generally takes the form: f(x)=1xnf(x) = \\frac{1}{x^n}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this specific case, the function is f(x)=1xf(x) = \\frac{1}{x}, which is evident from several key characteristics shown in the graph.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>1. Shape and Behavior<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">The curve is <strong>decreasing<\/strong> throughout the positive x-values and <strong>increasing negatively<\/strong> as x becomes more negative. This &#8220;L&#8221;-shaped behavior in the first and third quadrants is a hallmark of the reciprocal function. However, this particular graph only shows the <strong>first quadrant<\/strong> (positive x-values), which suggests the function shown is <strong>only for positive values of xx<\/strong> \u2014 meaning the domain is x&gt;0x &gt; 0.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>2. Vertical and Horizontal Asymptotes<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The graph <strong>never touches the x-axis<\/strong>, but it approaches it as x\u2192\u221ex \\rightarrow \\infty. This behavior indicates a <strong>horizontal asymptote at y=0y = 0<\/strong>.<\/li>\n\n\n\n<li>The graph rises steeply as it approaches x=0+x = 0^+, suggesting a <strong>vertical asymptote at x=0x = 0<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">These asymptotic behaviors are consistent with f(x)=1xf(x) = \\frac{1}{x}.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>3. Key Values<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">If you test a few x-values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>f(1)=11=1f(1) = \\frac{1}{1} = 1<\/li>\n\n\n\n<li>f(2)=12=0.5f(2) = \\frac{1}{2} = 0.5<\/li>\n\n\n\n<li>f(0.5)=10.5=2f(0.5) = \\frac{1}{0.5} = 2<\/li>\n\n\n\n<li>f(0.25)=4f(0.25) = 4<\/li>\n\n\n\n<li>f(0.125)=8f(0.125) = 8<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">These y-values match what is seen on the graph, confirming the function plotted is decreasing and rapidly approaching infinity as x approaches zero from the right.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Based on the curve\u2019s shape, asymptotes, and evaluated points, the function graphed is: f(x)=1x\\boxed{f(x) = \\frac{1}{x}}<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-506.jpeg\" alt=\"\" class=\"wp-image-227164\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which function is graphed below The Correct Answer and Explanation is: The graph shown represents the function: f(x)=1xf(x) = \\frac{1}{x} Explanation The graph provided is a classic representation of a reciprocal function, which generally takes the form: f(x)=1xnf(x) = \\frac{1}{x^n} In this specific case, the function is f(x)=1xf(x) = \\frac{1}{x}, which is evident from several [&hellip;]<\/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 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