{"id":28675,"date":"2025-06-20T14:23:50","date_gmt":"2025-06-20T14:23:50","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28675"},"modified":"2025-06-20T14:52:10","modified_gmt":"2025-06-20T14:52:10","slug":"for-each-function-graphed-below-state-whether-it-is-one-to-one","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/for-each-function-graphed-below-state-whether-it-is-one-to-one\/","title":{"rendered":"For each function graphed below,; state whether it is one-to-one"},"content":{"rendered":"\n

For each function graphed below,; state whether it is one-to-one One-to-one? Yes Yes No Yes One-to-one? Yes Yes No Yes X 2<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Here is the correct identification of whether each graphed function is one-to-one:<\/p>\n\n\n\n

Top Row (from left to right):<\/strong><\/p>\n\n\n\n

    \n
  1. No<\/strong><\/li>\n\n\n\n
  2. Yes<\/strong><\/li>\n\n\n\n
  3. No<\/strong><\/li>\n<\/ol>\n\n\n\n

    Bottom Row (from left to right):<\/strong><\/p>\n\n\n\n

      \n
    1. No<\/strong><\/li>\n\n\n\n
    2. No<\/strong><\/li>\n\n\n\n
    3. Yes<\/strong><\/li>\n<\/ol>\n\n\n\n

      A function is considered one-to-one<\/em> if every element of the range corresponds to exactly one element of the domain. Put another way, no two different x-values can produce the same y-value. The most common method to test for this is the horizontal line test<\/em>. If any horizontal line intersects the graph more than once, the function is not one-to-one.<\/p>\n\n\n\n

      Let\u2019s explore each case:<\/p>\n\n\n\n

        \n
      • Graph 1 (Top Left)<\/strong> appears to be a scatter plot without a consistent trend. Since several points share the same y-value with different x-values, the graph fails the horizontal line test. Therefore, it is not one-to-one.<\/li>\n\n\n\n
      • Graph 2 (Top Middle)<\/strong> is a straight line with a positive slope. It passes the horizontal line test because no horizontal line intersects it more than once. This graph represents a one-to-one function.<\/li>\n\n\n\n
      • Graph 3 (Top Right)<\/strong> shows a curve that increases and then decreases. This shape guarantees that some y-values are repeated for different x-values, so it is not one-to-one.<\/li>\n\n\n\n
      • Graph 4 (Bottom Left)<\/strong>, another scatter plot, displays similar issues as Graph 1 with repeated y-values. Hence, it is also not one-to-one.<\/li>\n\n\n\n
      • Graph 5 (Bottom Middle)<\/strong> is a piecewise function with segments that overlap in the vertical sense. Since multiple x-values lead to the same y-value within segments, it fails the test and is not one-to-one.<\/li>\n\n\n\n
      • Graph 6 (Bottom Right)<\/strong> is V-shaped but tilted diagonally. It passes the horizontal line test, so this function is<\/em> one-to-one.<\/li>\n<\/ul>\n\n\n\n

        Understanding these distinctions sharpens your grasp of function behavior and the geometry behind algebraic relationships.<\/p>\n\n\n\n

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

        For each function graphed below,; state whether it is one-to-one One-to-one? Yes Yes No Yes One-to-one? Yes Yes No Yes X 2 The Correct Answer and Explanation is: Here is the correct identification of whether each graphed function is one-to-one: Top Row (from left to right): Bottom Row (from left to right): A function is […]<\/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-28675","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28675","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=28675"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28675\/revisions"}],"predecessor-version":[{"id":28678,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28675\/revisions\/28678"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28675"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28675"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}