Question

reflecting the cubic function practice
complete this assessment to review what youve learned. it will not count toward your grade.
true or false: when given the function $f(x)=x^3$, the function $g(x)=-5f(x)$ will undergo a reflection due to its negative sign. enter 1 for true or 2 for false. (1 point)

Explanation:

Step1: Recall reflection rule

For a function \( y = f(x) \), a reflection over the x - axis is given by \( y=-f(x) \). Here, \( g(x)=- 5f(x) \), and the negative sign in front of the \( f(x) \) term indicates a reflection over the x - axis (since the transformation involves multiplying the function by a negative scalar, the reflection is part of the transformation due to the negative sign).

Step2: Analyze the given functions

We have \( f(x)=x^{3} \) and \( g(x)=-5f(x)=- 5x^{3} \). The negative sign in \( g(x) \) compared to \( f(x) \) means that the graph of \( g(x) \) is a reflection (over the x - axis) of the graph of \( f(x) \) (along with a vertical stretch by a factor of 5, but the negative sign does cause a reflection). So the statement is true.

Answer:

1