Question

given the function $f(x) = x^3 - 10$, which of the following functions is the new function after $f(x)$ is shifted 5 units up? (1 point)

$\bigcirc\\ h(x) = x^3 - 15$

$\bigcirc\\ h(x) = x^3 - 5$

$\bigcirc\\ h(x) = x^3 + 5$

$\bigcirc\\ h(x) = x^3 + 15$

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 \( f(x)=x^{3}-10 \), shift 5 units up: \( h(x)=f(x)+5=(x^{3}-10)+5 \).

Step3: Simplify the Expression

Simplify \( (x^{3}-10)+5 \) to \( x^{3}-5 \).

Answer:

\( h(x) = x^{3}-5 \) (corresponding to the option \( h(x)=x^{3}-5 \))