Question

Describe the transformation from v(x)=x3+2
to q(x)=(0.25x)3+2
.(1 point)
Responses

horizontal stretch by a factor of 4
horizontal stretch by a factor of 4

horizontal compression by a factor of 0.25
horizontal compression by a factor of 0.25

horizontal compression by a factor of 4
horizontal compression by a factor of 4

horizontal stretch by a factor of 0.25

Answer 1

To describe the transformation from \( v(x) = x^3 + 2 \) to \( q(x) = (0.25x)^3 + 2 \), we need to analyze the effect of the \( 0.25 \) coefficient applied to \( x \).

When we replace \( x \) with \( 0.25x \) in the function \( v(x) \), this indicates a **horizontal stretch**. The effect of multiplying \( x \) by a fraction (less than 1) compresses it, meaning that it takes the same output value at a larger input value.

Specifically, a factor of \( 0.25 \) means that for every x-value in \( v(x) = x^3 + 2 \), we must increase the x-value to \( 4x \) in order to maintain the same output. Therefore, the transformation involves a horizontal stretch by a factor of 4.

Thus, the correct response is:

**horizontal stretch by a factor of 4**.