Question

use transformations of the standard cubic function, f(x)=x³, to graph the function g(x)=x³+2. use the graphing tool to graph the function. click to enlarge graph

Explanation:

Step1: Identify parent function

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

Step2: Recognize transformation type

Vertical shift up by 2 units:
For any input $x$, $g(x) = f(x) + 2 = x^3 + 2$

Step3: Plot key points for $f(x)$

Key points of $f(x)=x^3$:
$(-2, -8)$, $(-1, -1)$, $(0, 0)$, $(1, 1)$, $(2, 8)$

Step4: Apply vertical shift to points

Add 2 to each y-coordinate:
$(-2, -8+2)=(-2, -6)$
$(-1, -1+2)=(-1, 1)$
$(0, 0+2)=(0, 2)$
$(1, 1+2)=(1, 3)$
$(2, 8+2)=(2, 10)$

Step5: Connect points smoothly

Draw a continuous curve through the transformed points.

Answer:

The graph of $g(x)=x^3+2$ is the graph of $f(x)=x^3$ shifted vertically upward by 2 units, passing through points $(-2, -6)$, $(-1, 1)$, $(0, 2)$, $(1, 3)$, $(2, 10)$ and following the cubic curve shape.