{"id":2293,"date":"2023-09-01T14:41:28","date_gmt":"2023-09-01T14:41:28","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=2293"},"modified":"2023-09-29T19:45:16","modified_gmt":"2023-09-29T19:45:16","slug":"psat-math-quiz-functions","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/psat\/psat-math-quiz-functions\/","title":{"rendered":"PSAT Math Quiz: Functions"},"content":{"rendered":"<p>Try the free practice questions in the quiz below and see how ready you are for Functions questions in the Math section on the Digital PSAT.<\/p>\n<p><strong>Content Review:<\/strong><\/p>\n<ul>\n<li><a title=\"PSAT Math: Functions\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-functions\/\"> PSAT Math: Functions <\/a><\/li>\n<li><a title=\"PSAT Math: Advanced Functions\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-functions-defined-by-tables-and-graphs\/\">PSAT Math: Advanced Functions<\/a><\/li>\n<li><a title=\"PSAT Math: Function Behavior and Transformations\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-function-behavior-and-transformations\/\">PSAT Math: Function Behavior and Transformations<\/a><\/li>\n<\/ul>\n<p><div  class='avia-builder-widget-area clearfix  avia-builder-el-0  el_before_av_promobox  avia-builder-el-first '><div id=\"custom_html-31\" class=\"widget_text widget clearfix widget_custom_html\"><div class=\"textwidget custom-html-widget\"><div><div class='op-interactive' id='63892e47886d59597a86b010' data-title='PSAT Math Quiz: Functions' data-url='https:\/\/kaplannorthamerica.outgrow.us\/63892e47886d59597a86b010?vHeight=1' data-width='100%'><\/div><script src='\/\/dyv6f9ner1ir9.cloudfront.net\/assets\/js\/nloader.js'><\/script><script>initIframe('63892e47886d59597a86b010');<\/script><\/div><\/div><\/div><\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-1  el_after_av_sidebar  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>PSAT Math Functions Question 1<\/strong><br \/>\nThe figure shows the graph of <i>r<\/i>(<i>x<\/i>). Which of the following cannot be a value of <i>x<\/i> for which <i>r<\/i>(<i>x<\/i>) = 0 ?<br \/>\n<a href=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2017\/08\/graph.png\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-23601\" src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2017\/08\/graph.png\" alt=\"past math\" width=\"576\" height=\"324\" \/><\/a><br \/>\nA. -3<br \/>\nB. -2<br \/>\nC. 2<br \/>\nD. 5<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-2  el_after_av_promobox  el_before_av_promobox \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-1\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-1\">Answer 1<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-1\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>A:\u00a0<\/strong>The notation <i>r(x) <\/i>= 0 means that the function is crossing the<i> x<\/i>-axis (has a <i>y<\/i>-value of 0), so look for the <i>x<\/i>-intercepts. The function <i>r(x)<\/i> intersects the <i>x<\/i>-axis at <i>x<\/i> = -2, 2, and 5. Because B, C, and D are all possible values, the correct answer is A.<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-3  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>PSAT Math Functions Question 2<\/strong><br \/>\nA construction company plans to build a long row of houses, each with a certain number of brown shingles on its roof. The number of brown shingles on a house\u2019s roof, <i>f<\/i>\u200a(<i>h<\/i>), is a function of its house number, <i>h<\/i>. The first few houses are shown here. If only brown shingles are used, how many shingles will the seventh house have?<br \/>\n<a href=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2017\/08\/psat.png\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-23603\" src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2017\/08\/psat.png\" alt=\"psat math\" width=\"576\" height=\"324\" \/><\/a><br \/>\nA. 7<br \/>\nB. 27<br \/>\nC. 46<br \/>\nD. 60<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-4  el_after_av_promobox  el_before_av_promobox \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-2\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-2\">Answer 2<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-2\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><div class=\"QuizQuestion-header\">\u00a0<strong>D:\u00a0<\/strong>Identifying the type of relationship between <i>h<\/i> and <i>f(h)<\/i> is key to solving this problem. The <i>f(h)\u00a0<\/i> values (shingle counts) are increasing at a variable rate, which rules out a linear function. The increase in <i>f(h)<\/i> is not significant with each increase in <i>h<\/i>, so exponential is not likely. A quadratic relationship is a good bet. Start with <i>f(h) = h^2. <\/i>That gives <i>f<\/i>(1) = 1^2 = 2, <i>f(<\/i>2) = 2^2 = 4, and <i>f<\/i>(3) = 3^2 = 9. Obviously this doesn\u2019t match the pattern, so ask yourself how much more <i>f<\/i>(h) needs to increase after squaring <i>h<\/i>; you\u2019ll see you need to add 11 to <i>h<\/i>^2 + 11 accurately depicts the relationship between <i>h<\/i> and <i>f(h)<\/i>. You\u2019re asked for the shingle count for the seventh house, so put 7 into your function: <i>f<\/i>(7) = 7^2 + 11 = 49 + 11 = 60, which matches (D).<\/div>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-5  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>PSAT Math Functions Question 3<\/strong><br \/>\nThe function <i>f<\/i>(<i>x<\/i>) = (<i>x<\/i> \u2212 4)\u00b2 is shown here. Which of the following correctly depicts the transformation <i>g<\/i>(<i>x<\/i>) = (\u2013<i>x<\/i> + 2)+ 3?<br \/>\n<a href=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2017\/08\/upload.png\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-23604\" src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2017\/08\/upload.png\" alt=\"psat math\" width=\"576\" height=\"324\" \/><\/a><\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-6  el_after_av_promobox  el_before_av_promobox \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-3\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-3\">Answer 3<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-3\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><div  class='avia-image-container  av-styling-    avia-builder-el-7  avia-builder-el-no-sibling  avia-align-center '  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\"  ><div class='avia-image-container-inner'><div class='avia-image-overlay-wrap'><img class='wp-image-44904 avia-img-lazy-loading-not-44904 avia_image' src=\"https:\/\/wpapp.kaptest.com\/study\/wp-content\/uploads\/Screenshot-2023-09-29-at-3.35.56-PM-2.png\" alt='' title='Screenshot-2023-09-29-at-3.35.56-PM-2' height=\"1098\" width=\"1370\"  itemprop=\"thumbnailUrl\"  \/><\/div><\/div><\/div>\n<p><strong>C:\u00a0<\/strong>Take each transformation one at a time. The negative sign inside the parentheses indicates a horizontal reflection (across the <i>y<\/i>-axis), so the parabola should still open up. Choice B has a vertical reflection (across the <i>x<\/i>-axis) and opens down, so you can eliminate it. The +3 outside the parentheses shifts <i>f(x)<\/i> up 3 units; D does not contain this component, so eliminate it as well. the +2 inside the parentheses is tricky: it means a <i>left<\/i> shift of 2 units, but it might be tempting to think you need to add 6 (and therefore move 6 units to the left) to get from <i>xI &#8211; 4 to <\/i>x + 2. Don\u2019t be fooled by this. Overall the graph will shift up 3 units, shift left 2 units, then reflect over the <i>y<\/i>-axis. Algebraically, your function would be <i>g(x)<\/i> = <i>(-x<\/i> &#8211; 2)^2 + 3 (not <i>g(x) <\/i>= (-<i>x<\/i> + 2)^2 + 3); this and the graphical analysis correspond to C, the correct answer.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-8  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p>\n<strong>PSAT Math Functions Question 4<\/strong><br \/>\nIf <i>f<\/i>\u200a(<i>x<\/i>) = \u2013<i>x<\/i> + 5 and <i>g<\/i>(<i>x<\/i>) = <i>x<\/i>\u200a<sup>2<\/sup>, which of the following is not in the range of <i>f<\/i>\u200a(<i>g<\/i>(<i>x<\/i>)) ?<br \/>\nA. -11<br \/>\nB. 0<br \/>\nC. 1<br \/>\nD. 9<\/p>\n<\/div><\/div><\/p>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-9  el_after_av_promobox  avia-builder-el-last \" >\n<section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-4\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-4\">Answer 4<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-4\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>D:\u00a0<\/strong>When dealing with a composition, the range of the inner function becomes the domain of the outer function, which in turn produces the range of the composition. In the composition <i>f(g(x))<\/i>, the function <i>g(x) <\/i>= <i>x<\/i>^2is the inner function. Every value of <i>x<\/i>, when substituted into this function, will result in a nonnegative value (because of the square on <i>x<\/i>). This means the smallest possible range value of <i>g(x)<\/i> is 0. Now look at <i>f(x)<\/i>. Substituting large positive values of <i>x<\/i> in the function will result in large negative numbers. Consequently, substituting the smallest value from the range of <i>g<\/i>, which is 0, results in the largest range value for the composition, which is -0 + 5 = 5. Because 9 &gt; 5, it is not in the range of <i>f(g(x))<\/i>, making D correct.<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div>\n<p><strong>Next:<\/strong> <a title=\"psat math\" href=\"https:\/\/www.kaptest.com\/study\/psat\/psat-math-quiz-tables-statistics-and-probability\/\">PSAT Math Quiz: Tables, Statistics, and Probability<\/a><br \/>\n<strong>Previous:<\/strong> <a title=\"PSAT Math Quiz: Exponents, Roots and Polynomials\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-quiz-exponents-roots-and-polynomials\/\">PSAT Math Quiz: Exponents, Roots, and Polynomials<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Try the free practice questions in the quiz below and see how ready you are for Functions questions in the Math section on the Digital PSAT. Content Review: PSAT Math: Functions PSAT Math: Advanced Functions PSAT Math: Function Behavior and Transformations Next: PSAT Math Quiz: Tables, Statistics, and Probability Previous: PSAT Math Quiz: Exponents, Roots, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":42026,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[240],"tags":[195,312,310,311],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2293"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=2293"}],"version-history":[{"count":10,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2293\/revisions"}],"predecessor-version":[{"id":44910,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2293\/revisions\/44910"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/42026"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=2293"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=2293"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=2293"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}