{"id":25913,"date":"2025-06-19T07:58:49","date_gmt":"2025-06-19T07:58:49","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25913"},"modified":"2025-06-19T07:58:50","modified_gmt":"2025-06-19T07:58:50","slug":"identify-a-horizontal-or-vertical-stretch-or-compression-of-the-function-fx-1-x-by-observing-the-equation-of-the-function-gx-5-x","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/identify-a-horizontal-or-vertical-stretch-or-compression-of-the-function-fx-1-x-by-observing-the-equation-of-the-function-gx-5-x\/","title":{"rendered":"Identify a horizontal or vertical stretch or compression of the function f(x) = 1\/x by observing the equation of the function g(x) = 5\/x."},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">Identify a horizontal or vertical stretch or compression of the function f(x) = 1\/x by observing the equation of the function g(x) = 5\/x. Answer choices: 1. A vertical compression by a factor of 5 2. A horizontal stretch by a factor of 5 3. A horizontal compression by a factor of 5 4. A vertical stretch by a factor of 5<\/pre>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: 4. A vertical stretch by a factor of 5<\/strong><\/p>\n\n\n\n<p>To determine whether the function transformation is a horizontal or vertical stretch or compression, we need to analyze how the function <strong>g(x) = 5\/x<\/strong> compares to the base function <strong>f(x) = 1\/x<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step Explanation:<\/h3>\n\n\n\n<p>The base function is:<br><strong>f(x) = 1\/x<\/strong><\/p>\n\n\n\n<p>The new function is:<br><strong>g(x) = 5\/x<\/strong><br>This can be rewritten as:<br><strong>g(x) = 5 \u00b7 f(x)<\/strong><\/p>\n\n\n\n<p>This means we are multiplying the <strong>entire function<\/strong> f(x) by 5. When a function is multiplied by a constant on the <strong>outside<\/strong>, it causes a <strong>vertical transformation<\/strong>.<\/p>\n\n\n\n<p>Specifically:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the constant is <strong>greater than 1<\/strong>, it causes a <strong>vertical stretch<\/strong>.<\/li>\n\n\n\n<li>If the constant is <strong>between 0 and 1<\/strong>, it causes a <strong>vertical compression<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Here, we are multiplying by 5, which is greater than 1. That means we are <strong>stretching<\/strong> the graph vertically. Every y-value from the original function <strong>f(x)<\/strong> becomes <strong>5 times larger<\/strong> in <strong>g(x)<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What it looks like:<\/h3>\n\n\n\n<p>Suppose <strong>f(2) = 1\/2<\/strong>.<br>Then <strong>g(2) = 5\/2<\/strong>.<\/p>\n\n\n\n<p>The x-value remains the same, but the output (y-value) is stretched vertically to 5 times the original height.<\/p>\n\n\n\n<p>This is not a <strong>horizontal<\/strong> transformation because we are not changing the x-value directly (like replacing <strong>x<\/strong> with <strong>5x<\/strong>, which would be a horizontal compression).<\/p>\n\n\n\n<p>Therefore, the correct transformation from <strong>f(x) = 1\/x<\/strong> to <strong>g(x) = 5\/x<\/strong> is a <strong>vertical stretch by a factor of 5<\/strong>. This makes the curve of the graph steeper by pulling it farther from the x-axis.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-14.jpeg\" alt=\"\" class=\"wp-image-25914\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-14.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-14-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Identify a horizontal or vertical stretch or compression of the function f(x) = 1\/x by observing the equation of the function g(x) = 5\/x. Answer choices: 1. A vertical compression by a factor of 5 2. A horizontal stretch by a factor of 5 3. A horizontal compression by a factor of 5 4. A [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-25913","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25913","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=25913"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25913\/revisions"}],"predecessor-version":[{"id":25915,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25913\/revisions\/25915"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25913"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}