Question

Describe how to translate the graph of y=√x to obtain the graph of y=√x-4

Answer 1

Answer:

Shifted to right by 4 units.

Step-by-step explanation:

We have been given a function $y=\sqrt{x}$. We are asked to find the translation rule to obtain the function $y=\sqrt{x-4}$ from $y=\sqrt{x}$.

Let us recall translation rules.

$f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}$  

$f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}$

$f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}$  

$f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}$

We can see that $-4$ is under radical, therefore, the function $y=\sqrt{x}$ is shifted to right by 4 units to obtain the graph of $y=\sqrt{x-4}$.

Answer 2

If the -4 is NOT under the radical sign the graph would move DOWN four units on the y axis.

If the -4 is under the radical sign the graph would move 4 units to the RIGHT on the x-axis.