Question

cubic & cube root functions unit online practice
complete this assessment to review what youve learned. it will not count toward your grade
which of the following is the equation of the new function h(x) that is obtained by shifting f(x) = (x + 9)^3 horizontally 10 units to the right? (1 point)
○ h(x) = (x + 9)^3
○ h(x) = (x + 19)^3
○ h(x) = (x + 1)^3
○ h(x) = (x - 1)^3

Explanation:

Step1: Recall Horizontal Shift Rule

For a function \( y = f(x) \), shifting horizontally \( a \) units to the right gives \( y = f(x - a) \).

Step2: Apply the Rule to \( f(x)=(x + 9)^3 \)

Here, \( a = 10 \), so substitute \( x \) with \( x - 10 \) in \( f(x) \):
\( h(x)=f(x - 10)=((x - 10)+ 9)^3=(x - 1)^3 \).

Answer:

\( h(x)=(x - 1)^3 \) (the last option, \( h(x)=(x - 1)^3 \))