Question

Can someone teach me piecewise functions?

Answer 1

if you have a good grasp of regular functions, this should be a simple concept

a piecewise function shows different behavior on different parts of its domain

as an example, we can take f(x) = |x| and turn it into a piecewise function by specifying its behavior on two different parts of its domain

f(x) = -x on the domain x (-infinity, 0)
and f(x) = x on the domain x (0, infinity)
and f(x) = 0 on x = 0

Answer 2

if you are asked to evaluate a piecewise function on some x-value, you have to look at the function definition, decide which interval your x-value falls in, and evaluate the function at that x-value

for example,


if you are given, say, x = 0, you look at the intervals x < -1, -1<x<2, and x>=2, x = 0 falls in the interval -1 < x < 2 so you would evaluate f(x) = x + 4 at x = 0

Answer 3

if you have any example problems you'd like to go over, I would be happy to