consider the following function. w(x)=(x + 4)^3 step 1 of 2: graph the original function by indicating how…

Explanation:

Step1: Identify the basic function

The basic function of $w(x)=(x + 4)^3$ is $y = x^3$.

Step2: Analyze the transformation

For the function $y=(x + 4)^3$, compared with $y = x^3$, we use the transformation rule for functions of the form $y=f(x + h)$. When $h = 4$ in $y=(x + 4)^3$ (where $f(x)=x^3$), according to the rule that if $y = f(x+h)$ and $h>0$, the graph of $y = f(x)$ is shifted $h$ units to the left. So the graph of $y=x^3$ is shifted 4 units to the left to get the graph of $w(x)=(x + 4)^3$.

Answer:

The graph of the basic function $y = x^3$ is shifted 4 units to the left to obtain the graph of $w(x)=(x + 4)^3$.