Question

cubic & cube root functions unit online practice
complete this assessment to review what you’ve learned. it will not count toward your grade.
given the function $f(x) = x^3 - 1$, which of the following functions is the new function $h(x)$ after $f(x)$ is shifted 10 units up? (1 point)

• $h(x) = x^3 + 10$
• $h(x) = x^3 + 9$
• $h(x) = x^3 - 11$
• $h(x) = x^3 - 9$

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = f(x) \), shifting it \( k \) units up gives \( y = f(x)+k \) (where \( k>0 \)).

Step2: Apply the Rule to \( f(x) \)

Given \( f(x)=x^{3}-1 \) and we shift it 10 units up. So \( h(x)=f(x) + 10 \).
Substitute \( f(x)=x^{3}-1 \) into the formula: \( h(x)=(x^{3}-1)+10 \).

Step3: Simplify the Expression

Simplify \( (x^{3}-1)+10 \): \( x^{3}+(- 1 + 10)=x^{3}+9 \).

Answer:

\( h(x)=x^{3}+9 \) (the second option: \( h(x)=x^{3}+9 \))