Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

True or False 

To obtain the graph of $f\left(x\right)=\sqrt{x+2}$, shift the graph of $y=\sqrt{x}$ horizontally to the right $2$ units.

Step-by-Step Solution

Answer

False

Step 1. Concept Used

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 right $h$ units.

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.

Step 2. Identify true or false

As $2$ is added to the argument $x$ of the function $y=\sqrt{x}$, to get a new function $f\left(x\right)=\sqrt{x+2}$.

So by the rule horizontal translation the graph of $f\left(x\right)=\sqrt{x+2}$ is obtained by shifting the graph of$y=\sqrt{x}$ horizontally to the left $2$ units.

So the given statement is false.