Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

True or False 

To obtain the graph of $f\left(x\right)=x^3+5,$ shift the graph of $y=x^3$ vertically up $5$ units.

Step-by-Step Solution

Answer

The given statement is true.

Step 1. Given Information

There is the graph of $f\left(x\right)=x^3+5.$

We have to tell whether the statement is true or false if we shift the graph of $y=x^3$ vertically up $5$ units.

Step 2. Analyze the graph

The concept is if a positive real number k is added to the outputs of a function $y=f\left(x\right),$ the graph of the new function $y=f\left(x\right)+k$ is the graph of f shifted vertically up k units.

So, if $5$ is added to the outputs of a function $y=x^3$, the graph of the new function $f\left(x\right)=x^3+5$ is the graph of function shifted vertically up $5$units.

Therefore, the statement is true.