PIECEWISE FUNCTIONS
Functions that are represented by two or more pieces are
called piecewise functions. Each part of a piecewise
function can be described using a specific equation for a
specific interval of the domain.
EX.
f(x) =
– x2, if x < 0
–x + 1, if x  0
(NOTE: closed dot  vs. open dot 
to show inclusion!!)
If the pieces of the function do not join together at the endpoints of the given
intervals, then the function is discontinuous at these values of the domain.
Ex.
f(x) is discontinuous at x = 0.
If all the pieces of the function do join together at the endpoints of the given
intervals, then the function is continuous.
EX.
f(x) =
x2 + 1, if x < 2
2x + 1, if x  2
Do the functions have the same y-values
at the points where they are pieced together?
Ex 
a)
Graph the given piecewise function.
y
2x – 3, if x  1
f(x) =
x – 2, if 1 < x  4
2
(x – 3) + 2, if x > 4
0
b)
Ex 
x
Determine where the function is discontinuous and continuous.
Write the algebraic representation of the given piecewise function, using
function notation:
f(x) =
Homework: p.51–53 #1adf, 2–4, 5acd, 8, 14