Question

In Problems 5, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.

$f\left(x\right)=(x+2{)}^3$

Short answer

The graph is shown below:

Step-by-step solution

Given information

The given function is$f\left(x\right)=(x+2{)}^3$.

Graph the base function

To help establish the graph, find the points at $x=-2,x=0$and $x=2$.

$\begin{array}{rcl}y& =& {\left(-2\right)}^3\\ & =& 8\\ y& =& {\left(0\right)}^3\\ & =& 0\\ y& =& {\left(2\right)}^3\\ & =& 8\end{array}$

The graph is shown below:

Graph the given function

Shift the previous graph $2$units to the left to get the desired graph for the given function $f\left(x\right)$.

To help establish the graph, determine three points by subtracting 2 from the $x$-coordinates of the points in step 2.

Maintain the $y$-coordinates of these points.

The given function graph is shown below:

Write the conclusion

The graph of the given function is shown below: