Question

Use the image to answer the question.

Two curves are drawn on a coordinate plane. The x-axis ranges from negative 10 to 10 in one-unit increments and the y-axis ranges from negative 5 to 5 in one-unit increments.
▼Click for Long Desc
A solid curve starts at left parenthesis 0 comma negative 2 right parenthesis, rises slightly and passes through left parenthesis 1 comma negative 0.7 right parenthesis, left parenthesis 2 comma 0 right parenthesis, and continues rightward and slightly upward, passing through left parenthesis 4 comma 0.5 right parenthesis, left parenthesis 7 comma 1 right parenthesis, and left parenthesis 10 comma 1.5 right parenthesis. A dotted curve rises from left parenthesis 0 comma negative 2 right parenthesis, ascends through left parenthesis 2 comma negative 0.5 right parenthesis, left parenthesis 6 comma 0 right parenthesis, and left parenthesis 10 comma 0.3 right parenthesis. All values are approximate.

The solid orange graph represents the original function and the dotted blue graph represents the dilated function. Which of the following correctly identifies the value of k and describes whether it is a compression or a stretch transformation?

(1 point)
Responses

3; compression
3; compression

3; stretch
3; stretch

1/3
; compression
Start Fraction 1 over 3 End Fraction ; compression

1/3
; stretch

Answer 1

Answer: 3; stretch.

Reason: The original has f(2)=0 while the dilated has g(6)=0, so x-values are multiplied by 3 (6 = 3·2). Thus g(x)=f(x/3), a horizontal stretch by factor 3.