Question

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

Answer 1

`I`, `III` and `IV` quadrants and it passes through y-axis at `(0,-sqrt(5))` and x-axis at `(sqrt(21)/2+1/2,0)`.

Explanation:

graph{x-sqrt(x+5) [-6.407, 7.64, -5.67, 1.356]}

As you can see the graph passes through `I`, `III` and `IV` quadrants.

To know the y-axis point you have to substitute de `x` by `0`. So:
`f(x)=x-sqrt(x+5) ➝ f(0)=0-sqrt(0+5)=-sqrt(5)≈-2.236`
And you get the point `(0,-sqrt(5))`.

To know the x-axis point(s) you have to equal the function to `0`. So:
`f(x)=x-sqrt(x+5)=0`
you isolate the variable `x`:
`x=sqrt(21)/2+1/2≈2.79`
So you get the point `(sqrt(21)/2+1/2,0)`.