Question

use transformations of the standard cubic function, f(x)=x³, to graph the function g(x)=x³+4. use the graphing tool to graph the function. click to enlarge graph

Explanation:

Step1: Identify base function

Base function: $f(x) = x^3$

Step2: Recognize transformation type

$g(x) = f(x) + 4$, so this is a vertical shift up by 4 units.

Step3: Transform key points of $f(x)$

For $f(x)=x^3$, key points are:

• When $x=-2$, $f(-2)=(-2)^3=-8$, so transformed point: $(-2, -8+4)=(-2, -4)$
• When $x=0$, $f(0)=0^3=0$, so transformed point: $(0, 0+4)=(0, 4)$
• When $x=2$, $f(2)=2^3=8$, so transformed point: $(2, 8+4)=(2, 12)$

Step4: Plot and connect points

Plot $(-2,-4)$, $(0,4)$, $(2,12)$ and draw a smooth cubic curve through them, matching the shape of $f(x)=x^3$ but shifted up 4 units.

Answer:

The graph of $g(x)=x^3 + 4$ is the graph of $f(x)=x^3$ shifted vertically upward by 4 units, passing through key points $(-2,-4)$, $(0,4)$, and $(2,12)$.