Question

What is the domain and range of `f(x) = sqrt(x^2-36)`?

Answer 1

Domain: `x <= -6` and `x >= 6`
Range: all real y

Explanation:

graph{sqrt(x^2-36) [-10, 10, -5, 5]}

From the graph,
Domain: `x <= -6` and `x >= 6`
Range: all real y

You can also think about the domain as the part where the x-value has a corresponding y-value

Say you sub x=5, you will not get a solution because you cannot squareroot a negative number so you know that your domain should not include a x=5