Q. 20 - Precalculus Enhanced with Graphing Utilities

Question

In Problems $19-26,$ write the function whose graph is the graph of $y=x^3$ but is:

Shifted to the left $4$ units 

Step-by-Step Solution

Answer

The function is $y={(x+4)}^3.$

Step 1. Given Information

It is given that the function whose graph is the graph of $y=x^3$ but it is shifted to the left by $4$ units. 

Step 2. Stating the function of the graph

If the argument x of a function f  is replaced by $x+h, h>0,$ the graph of the new function $y=f(x+h)$ is the graph of f shifted horizontally left h units.

Since the graph is shifted to the left by $4$ units, the function of the graph is $y={(x+4)}^3.$