Looking at the table:<\/p>\n\n\n\n
- \n
- f(0)=\u22123f(0) = -3f(0)=\u22123
This function does not<\/strong> have an initial value of 3, so the table is not correct<\/strong>.<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 2: Check the equation f(x)=13(9)xf(x) = \\frac{1}{3}(9)^xf(x)=31\u200b(9)x.<\/strong>
Let\u2019s plug in x=0x = 0x=0:f(0)=13(9)0=13(1)=13f(0) = \\frac{1}{3}(9)^0 = \\frac{1}{3}(1) = \\frac{1}{3}f(0)=31\u200b(9)0=31\u200b(1)=31\u200b<\/p>\n\n\n\nSo, this function has an initial value of 13\\frac{1}{3}31\u200b, not<\/strong> 3.<\/p>\n\n\n\n
\n\n\n\nStep 3: Check the graph.<\/strong>
Look at where the graph crosses the y-axis. The y-axis is where x=0x = 0x=0.
From the graph, we see that when x=0x = 0x=0, y=3y = 3y=3.
So:f(0)=3f(0) = 3f(0)=3<\/p>\n\n\n\nThat matches our condition.<\/p>\n\n\n\n
\n\n\n\nStep 4: Check the equation f(x)=3xf(x) = 3^xf(x)=3x.<\/strong>
Plug in x=0x = 0x=0:f(0)=30=1f(0) = 3^0 = 1f(0)=30=1<\/p>\n\n\n\nSo, this function also does not<\/strong> have an initial value of 3.<\/p>\n\n\n\n
\n\n\n\nFinal Conclusion:<\/h3>\n\n\n\n
Only the graph<\/strong> represents an exponential function with an initial value of 3. Therefore, it is the correct answer.<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-202.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"Which exponential function has an initial value of 3? x f(x) -2 -3.938 -1 -3.75 0 -3 1 0 2 12 y 8 6 4 2 x -3 -2 -1 1 2 3 Step 1: Check the table.Looking at the table: Step 2: Check the equation f(x)=13(9)xf(x) = \\frac{1}{3}(9)^xf(x)=31\u200b(9)x.Let\u2019s plug in x=0x = 0x=0:f(0)=13(9)0=13(1)=13f(0) = […]<\/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-233184","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233184","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=233184"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233184\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233184"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}