Question

Find the domain and range.

D: {___ < x < ___}
R: {___ < y < ___}
it can also be the less than or equal to sign.

Answer 1

The domain of the graph is 1 < x < 3, and the range is -1 < y

How to find the domain and range?

First let's find the domain, this is the set of possible inputs that we can use in the function.

To identify the domain we need to look at the horizontal axis of the graph, we can see that:

In the left we have a vertical asymptote at x = 1

In the right we have a open circle at x = 3

So the domain is 1 < x < 3

Now for the range we need to look at the vertical axis, we can see that we have the lower value at y = -1 (again with an open circle, so it does not belong to the range)

Then the graph goes up (this means we don't have an upper bound). Then the range is:

R: -1 < y