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?

Question

(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 stretched by a factor of 14.
The parent function has been vertically stretched 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. 

Answer 1

The transformed function \( y = 4f(x) \) indicates that the graph of the parent function \( f(x) \) is vertically stretched by a factor of 4. This is because multiplying the output of the function \( f(x) \) by 4 results in values that are four times larger, which effectively stretches the graph away from the x-axis.

Therefore, the correct response is:

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