Question

In Problems 7, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.

$f\left(x\right)=(x-1{)}^4+2$

Short answer

The graph is shown below:

Step-by-step solution

Given information

The given function is$f\left(x\right)=(x-1{)}^4+2$

Graph the base function

Graph the base function $y=x^4$.

To help establish the graph, find the points at $x=-1,x=0$and $x=1$.

$\begin{array}{rcl}y& =& {\left(-1\right)}^4\\ & =& 1\\ y& =& {\left(0\right)}^4\\ & =& 0\\ y& =& {\left(1\right)}^4\\ & =& 1\end{array}$

The graph is shown below:

Graph the function fx=x-14

Shift the previous graph 1 unit to the right to get the graph for $y=(x-1{)}^4$.

To help establish the graph, determine three points by adding 1 from the $x$-coordinates of the points in step $1$

Maintain the $y$-coordinates of these points.

Graph the given function

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

To help establish the graph, determine three points by adding 2 to the $y$-coordinates of the points in step $2$

Maintain the $x$-coordinates of these points.

Write the conclusion

The graph of the given function is shown below: