Question

In Problems 27– 40, use transformations of the graph of $y=x^4$or $y=x^5$to graph each function. Verify your results using a graphing utility.

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

Short answer

The graph of the function $f\left(x\right)={\left(x+1\right)}^4$is shown in the figure below and move to one unit left as compare to$f\left(x\right)=x^4$.

Step-by-step solution

Step 1. Given Information

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

Step 2. First draw the graph of y=x4

Step 3. Shift the graph one unit left to the origin

Step 4. Draw a table for values of x,y

x	-3	$-2$	-1	0	1	2	3	4	5
y	16	1	0	1	16	81	256	625	1296

Step 5. Plot these points on the Cartesian plane and connect them