Question

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

Answer 1

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.

Answer 2

Shifted to right by 4 units.

Explanation:

We have been given a function
`y=√(x)`. We are asked to find the translation rule to obtain the function
`y=√(x-4)` from
`y=√(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=√(x)` is shifted to right by 4 units to obtain the graph of
`y=√(x-4)`.