Question

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

Answer 1

See answer below

Explanation:

Given: `f(x) = |2x + 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: " all Reals"`

The range is the valid outputs: `y, " "y >= 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 `" "y >= 0`

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