Question

If f(x)=x3
, what is the effect on its graph when f(x)
is replaced by f(−2x)
?(1 point)
Responses

a horizontal compression and reflection over the y-axis
a horizontal compression and reflection over the y -axis

a vertical stretch and reflection over the x-axis
a vertical stretch and reflection over the x -axis

a horizontal stretch and reflection over the y-axis
a horizontal stretch and reflection over the y -axis

a vertical compression and reflection over the x-axis

Answer 1

To analyze the effect of replacing \( f(x) \) with \( f(-2x) \) when \( f(x) = x^3 \), let's break it down:

1. **Reflected over the y-axis**: The negative sign in \( -2x \) indicates a reflection across the y-axis. This means that the graph of the function is flipped over the y-axis.

2. **Horizontal compression**: The factor of 2 in \( -2x \) indicates a horizontal compression by a factor of 2. This means that the graph is squeezed towards the y-axis.

Putting both effects together, the transformation \( f(-2x) \) causes the graph of \( f(x) = x^3 \) to undergo a horizontal compression by a factor of 2 and a reflection over the y-axis.

Therefore, the correct answer is:

**a horizontal compression and reflection over the y-axis.**