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.

Short answer

False

Step-by-step solution

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.