Question

How do you find the domain of `f(x) = |2x + 1|`?

Answer 1

`-oo < x < oo`

Explanation:

The domain is the set of `x` values that an equation can take.

The range is the set of `y` values an equation can spit out.

For `f(x) = |2x+1|`, you can put in any `x` value and get a `y` out, so the domain is anything:

`-oo < x < oo`

However, because it is the ultimate value (or modulus) function, it is the positive distance from zero - in other words, if the output is negative, it becomes positive, and if it is positive, is stays positive.

Therefore, it can only be positive, so the range is:

`f(x) >= 0`