Question

Which quadrants and axes does `f(x)=5+sqrt(x+12)` pass through?

Answer 1

The domain of this function is clearly `x ≥ -12`.

The range of the function is `y ≥ 5`.

Therefore, the function passes through the first and second quadrants and only over the y-axis.

We can confirm graphically:

graph{5 + sqrt(x +12) [-25.65, 25.65, -12.83, 12.83]}

Hopefully this helps!