Question

fill in the blanks to correctly complete the sentence
to obtain the graph of $f(x)=(x+6)^3 - 2$, shift the graph of $y=x^3$ to the left __ units and down __ units.

to obtain the graph of $f(x)=(x+6)^3 - 2$, shift the graph of $y=x^3$ to the left $square$ units and down $square$ units.

Explanation:

Step1: Analyze horizontal shift rule

For $f(x)=(x+h)^3$, shift left by $h$ units. Here, $h=6$.

Step2: Analyze vertical shift rule

For $f(x)=x^3 - k$, shift down by $k$ units. Here, $k=2$.

Answer:

To obtain the graph of $f(x)=(x+6)^3 - 2$, shift the graph of $y=x^3$ to the left $\boldsymbol{6}$ units and down $\boldsymbol{2}$ units.