Question

shifting the cubic function quick check
given the function $f(x) = x^3 + 5$, which of the following functions is the new function after $f(x)$ is shifted 3 units up? (1 point)
$\bigcirc\\ h(x) = x^3 - 5$
$\bigcirc\\ h(x) = x^3 + 5$
$\bigcirc\\ h(x) = x^3 + 8$
$\bigcirc\\ h(x) = x^3 - 8$

Explanation:

Step1: Recall Vertical Shift Rule

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

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

Given \( f(x)=x^{3}+5 \) and shifting 3 units up, so \( h(x)=f(x)+3 \).
Substitute \( f(x) \): \( h(x)=(x^{3}+5)+3 \).
Simplify: \( h(x)=x^{3}+8 \).

Answer:

\( h(x) = x^{3}+8 \) (the third option, i.e., \( h(x)=x^{3}+8 \))