{"id":42203,"date":"2025-06-28T16:54:34","date_gmt":"2025-06-28T16:54:34","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42203"},"modified":"2025-06-28T16:54:35","modified_gmt":"2025-06-28T16:54:35","slug":"fxx2-vertical-shrink-by-a-factor-of-1-2-and-a-reflection-in-the-y-axis-followed-by-a-translation-1-unit-down","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/fxx2-vertical-shrink-by-a-factor-of-1-2-and-a-reflection-in-the-y-axis-followed-by-a-translation-1-unit-down\/","title":{"rendered":"f(x)=x^2; vertical shrink by a factor of 1\/2 and a reflection in the y-axis, followed by a translation 1 unit down"},"content":{"rendered":"\n

f(x)=x^2; vertical shrink by a factor of 1\/2 and a reflection in the y-axis, followed by a translation 1 unit down<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To transform the function f(x)=x2f(x) = x^2f(x)=x2 as described, we need to apply each transformation step by step. Let\u2019s break it down:<\/p>\n\n\n\n

    \n
  1. Vertical Shrink by a Factor of 12\\frac{1}{2}21\u200b:<\/strong>
    A vertical shrink by a factor of 12\\frac{1}{2}21\u200b means that the output values (the yyy-values) of the function are halved. This can be achieved by multiplying the function by 12\\frac{1}{2}21\u200b. The function becomes: f(x)=12x2f(x) = \\frac{1}{2} x^2f(x)=21\u200bx2 This transformation reduces the height of the graph by half.<\/li>\n\n\n\n
  2. Reflection in the y-axis:<\/strong>
    A reflection across the yyy-axis involves changing the sign of the xxx-variable. Mathematically, this can be represented by replacing xxx with \u2212x-x\u2212x in the function. The function becomes: f(x)=12(\u2212x)2f(x) = \\frac{1}{2} (-x)^2f(x)=21\u200b(\u2212x)2 Since squaring \u2212x-x\u2212x still results in x2x^2×2, the function simplifies to: f(x)=12x2f(x) = \\frac{1}{2} x^2f(x)=21\u200bx2 This step doesn\u2019t affect the graph of the function because squaring xxx or \u2212x-x\u2212x produces the same result. Hence, the graph is still symmetric about the yyy-axis.<\/li>\n\n\n\n
  3. Translation 1 Unit Down:<\/strong>
    A translation of 1 unit down means we subtract 1 from the function. The new function becomes: f(x)=12×2\u22121f(x) = \\frac{1}{2} x^2 – 1f(x)=21\u200bx2\u22121 This shifts the entire graph of the function downward by 1 unit.<\/li>\n<\/ol>\n\n\n\n

    Final Function:<\/h3>\n\n\n\n

    After applying all these transformations, the final function is:f(x)=12×2\u22121f(x) = \\frac{1}{2} x^2 – 1f(x)=21\u200bx2\u22121<\/p>\n\n\n\n

    Explanation:<\/h3>\n\n\n\n

    The transformations applied to the original function f(x)=x2f(x) = x^2f(x)=x2 are straightforward:<\/p>\n\n\n\n

      \n
    • The vertical shrink reduces the amplitude of the parabola, making it “flatter.”<\/li>\n\n\n\n
    • The reflection across the yyy-axis doesn\u2019t change the shape since the original function is already symmetric about the yyy-axis.<\/li>\n\n\n\n
    • The downward translation shifts the entire graph 1 unit lower, maintaining the shape but adjusting the position on the coordinate plane.<\/li>\n<\/ul>\n\n\n\n

      Thus, the overall transformation results in a parabola that is narrower than the original (due to the vertical shrink), symmetric about the yyy-axis (since the reflection doesn’t change the graph), and shifted down by 1 unit.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      f(x)=x^2; vertical shrink by a factor of 1\/2 and a reflection in the y-axis, followed by a translation 1 unit down The Correct Answer and Explanation is: To transform the function f(x)=x2f(x) = x^2f(x)=x2 as described, we need to apply each transformation step by step. Let\u2019s break it down: Final Function: After applying all these […]<\/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-42203","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42203","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=42203"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42203\/revisions"}],"predecessor-version":[{"id":42205,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42203\/revisions\/42205"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=42203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=42203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=42203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}