Question

Why is an absolute value transformation an example of a piecewise function?

Answer 1

an absolute value function a piecewise function because of how it's defined


|x| = x if x >= 0

OR

|x| = -x if x < 0

Answer 2

for instance

replace 'x' with 3 to get

|3| = 3

we're using the rule |x| = x since 3 is greater than 0

Answer 3

or

if x = -10, then we use the rule |x| = -x and we get

|x| = -x

|-10| = -(-10)

|-10| = 10

Answer 4

so put together into a piecewise function, we get this

\[\large |x| = \begin{cases}x \ \ \ \ \text{ if } x \ge 0\\-x \ \ \ \text{ if } x < 0 \end{cases}\]