Question

How do you write `f(x) = |2x+3|` as a piecewise function?

Answer 1

Use the definition:
`|f(x)| = {(f(x)", "f(x) >= 0),(-f(x)", "f(x) < 0):}`

Explanation:

Given `f(x) = |2x+3|`

Using the definition:

`f(x) = |2x+3| = {(2x+3", "2x+3 >= 0),(-2x-3", "2x+3 < 0):}`

It is good practice to simplify the inequalities:

`f(x) = {(2x+3", "2x >= -3),(-2x-3", "2x < -3):}`

Finished:

`f(x) = {(2x+3", "x >= -3/2),(-2x-3", "x < -3/2):}`