Question

shifting the cubic function practice
complete this assessment to review what you’ve learned. it will not count toward your grade.
true or false? given the function $f(x) = x^3$, the graph of the function $h(x) = f(x) + 10$ is the graph of $f(x)$ shifted 10 units vertically upwards.
option #1: true
option #2: false
(1 point)

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = f(x) \), the transformation \( y = f(x)+k \) (where \( k \) is a constant) shifts the graph vertically. If \( k>0 \), it shifts \( k \) units upward; if \( k < 0 \), it shifts \( |k| \) units downward.

Step2: Apply Rule to Given Function

Here, \( f(x)=x^{3} \) and \( h(x)=f(x) + 10 \), so \( k = 10>0 \). By the vertical shift rule, adding 10 to \( f(x) \) shifts the graph of \( f(x) \) 10 units upward.

Answer:

Option #1: True