# How do you find domain and range for  f(x) =abs(2x+1)?

Jul 2, 2018

#### Explanation:

Given: $f \left(x\right) = | 2 x + 1 |$

To find the domain and range analytically, you would need to know that an absolute value only allows positive values for the output.

Any $x$ value selected would only give zero or positive values for $y$. This means

The domain is the valid inputs: $x : \text{ all Reals}$

The range is the valid outputs: $y , \text{ } y \ge 0$

You can also find the domain and range by graphing the function and seeing that there are no negative $y$ values. This means the range would be $\text{ } y \ge 0$

graph{abs(2x+1) [-5, 5, -5, 5]}