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Question

A coordinate plane shows two v-shaped curves.

The function graphed with a solid line is the parent function, y=f(x)
. Which of the following describes the transformed function, y=4f(x)
, which is shown with a dotted line?

(1 point)
Responses

The parent function has been vertically compressed by a factor of 14.
The parent function has been vertically compressed by a factor of Start Fraction 1 over 4 End Fraction .

The parent function has been vertically compressed by a factor of 4.
The parent function has been vertically compressed by a factor of 4.

The parent function has been vertically stretched by a factor of 4.
The parent function has been vertically stretched by a factor of 4.

The parent function has been vertically stretched by a factor of 14.
The parent function has been vertically stretched by a factor of Start Fraction 1 over 4 End Fraction .
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Answer 1

To determine the relationship between the parent function \( y = f(x) \) and the transformed function \( y = 4f(x) \), we need to analyze how the transformation affects the function.

In the expression \( y = 4f(x) \), the coefficient \( 4 \) indicates that the function \( f(x) \) is being vertically stretched. Specifically, every output value \( f(x) \) is being multiplied by \( 4 \), which means that the height of the graph is increased.

Therefore, the correct description of the transformation is:

The parent function has been vertically stretched by a factor of 4.