Question

What is the domain of this function? I already tried (-inf,-2) it was wrong.

Answer 1

Hello!

First off, (-inf, -2) was half of the domain, so you were right on track, but almost there!

Since this function has a vertical asymptote at x = -2, any x-values that are equal to -2 cause the function to be undefined. So, we show that as (-∞, -2) because this function is a continuous function from that interval.

Since this function is also continuous from the interval -2 to ∞, we show that as the second part of our domain; written as (-2, ∞).

Remember that parentheses and brackets have different meanings when using them to state the domain/range of a function. Parentheses are used to not include that value, while brackets are used to include it.

In that case, we need to combine this two intervals using the "union" symbol, which is "U".

Therefore, the domain of the function is (-∞, -2) U (-2, ∞).