Question

the function f(x)= sqrt x is translated left 5 units and up 3 units to create the function g(x). what is the domain of g(x)?

Answer 1

x ≥ -5

Explanation:

If we have a translation to left c units, we write " x + c " in the function, and

If we have a translation to right c units, we write " x - c" in the function

If we have vertical translation up b units, we "add b to the function", and

If we have vertical translation down b units, we "subtract b to the function"

The parent function is
`f(x)=√(x)`

Since translation left 5 units and up 3 units, we can write:

`f(x)=√(x+5) + 3`

The domain is affected by the square root sign and we know the number under the square root CANNOT be negative, so we can say:

x + 5 ≥ 0

x ≥ -5

This is the domain.