Question

Find the domain of the following graph:

−7 < x ≤9


−7 < y ≤ 9


−7 < x ≤5


−7 < y ≤ 5

Answer 1

`-7<x\leq 9`

Explanation:

The domain is the set of all x-values. We can find the domain by finding the left boundary of the graph (the furthest left x-value) and then the right boundary (the furthest right x value).

The furthest left x-value is -7. Notice it has a large open circle here that is not filled in. This means the function does not include -7 but includes numbers very close to it like-6.999999..... We sue use an inequality sign without an equal to to write -7. x >-7.

The furthest right x value is 9. It has a closed circle or "filled in" circle so we write with an equal to sign.
`x\leq 9`.

We combine the two into
`-7<x\leq 9`.