Question

Which quadrants and axes does `f(x)=5sqrt(x+5)` pass through?

Answer 1

This is a domain and range question.

Explanation:

A radical function can only have a non-negative argument and a non-negative outcome.
So `x+5>=0->x>=-5` and also `y>=0`
This means that `f(x)` can only be in the first and second quadrant.

Since the function is positive when `x=0` it will cross the `y`-axis.
Since `f(x)=0` when `x=-5` it will touch (but not cross) the `x`-axis
graph{5*sqrt(x+5) [-58.5, 58.5, -29.26, 29.3]}