Question

If you apply the below transformations to the square root parent function,

F(x) = VX, what is the equation of the new function?
• Shift 12 units right.
• Shift seven units down.

Answer 1

We have the following function:
`f(x) =√(x)`

We know that given a function f(x), the function g(x) = f(x+m) is exactly the same function f(x) but shifted m units to the left.

Therefore, to shift the function 12 units right we should:

`f(x) =√(x)` ⇒
`f(x-12) =√(x-12)`

We know that given a function f(x), the function g(x) = f(x)+m is exactly the same function f(x) but shifted m units up.

Therefore, to shift seven units down we should:

`f(x) =√(x)` ⇒
`f(x) =√(x)-7`