Which of the following statements correctly describes how the parent function f(x)=|x| was dilated to result in the graphed function? The function was multiplied by .5 (1 point) Responses The parent function was vertically translated down. The parent function was vertically translated down. The parent function was horizontally compressed. The parent function was horizontally compressed. The parent function was vertically translated up. The parent function was vertically translated up. The parent function was horizontally stretched.

Question

Which of the following statements correctly describes how the parent function f(x)=|x| was dilated to result in the graphed function? The function was multiplied by .5  (1 point) Responses The parent function was vertically translated down. The parent function was vertically translated down. The parent function was horizontally compressed. The parent function was horizontally compressed. The parent function was vertically translated up. The parent function was vertically translated up. The parent function was horizontally stretched.

GPT-4o mini · Answer

To determine how the parent function $ f(x) = |x| $ has been dilated to result in a different function, we need to analyze the effects of dilations on the graph of the function. If the function has been multiplied by 0.5, it would imply a vertical compression. The transformation would take the form: $$ g(x) = 0.5|x| $$ This transformation compresses the values of the function toward the x-axis, making the graph flatter than the parent function $ f(x) = |x| $. So, if the graph you are looking at is indeed the result of multiplying the parent function by 0.5, then the correct description would be: **The parent function was vertically compressed.** Thus, among your choices, the appropriate response is not explicitly listed, but it is important to note that if the function was altered, multiplying by 0.5 suggests a vertical compression. Ensure the specifics of your graph reflect this if necessary.