Question

Use the image to answer the question.

An upward parabola with arrows at both the ends passes through 3 plotted points. The x-axis ranges from negative 5 to 5 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments.
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The coordinates of the plotted points are labeled as follows: left parenthesis negative 1 comma 9 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 1 comma 9 right parenthesis.

Which of the following statements correctly describes how the parent function f(x)=x^2
has been dilated to produce the graph?

(1 point)
Responses

A) The parent function f(x)=x^2
has been horizontally compressed.
The parent function f left parenthesis x right parenthesis equals x squared has been horizontally compressed.

B) The parent function f(x)=x^2
has been vertically translated up.
The parent function f left parenthesis x right parenthesis equals x squared has been vertically translated up.

C) The parent function f(x)=x^2
has been vertically translated down.
The parent function f left parenthesis x right parenthesis equals x squared has been vertically translated down.

D) The parent function f(x)=x^2
has been horizontally stretched.

Answer 1

A

The graph is g(x)=9x^2 (since g(1)=9), and 9x^2 = (3x)^2 = f(3x), so the parabola is horizontally compressed by a factor of 1/3.