4-1: Intro to Piecewise-Defined Functions

4-1: Intro to Piecewise-Defined Functions
Objectives:
1. To evaluate, write,
and graph piecewise
functions
Assignment:
• P. 60: 14-17
• P. 71: 1-9
• Challenge Problems
Objective 1
You will be able to
evaluate, write, and
graph piecewise
functions
Exercise 1a
Determine whether
the graph shown
represents a
function.
Exercise 1b
3
−2𝑥
Graph 𝑦 =
− 1 for 𝑥 < −2, 𝑦 = 𝑥 − 1 for
− 2 ≤ 𝑥 ≤ 1, and 𝑦 = 3 for 𝑥 > 1 on the
same coordinate grid.
Piecewise Functions
A piecewise function is defined by more
than one equation. Each equation
corresponds to a different part of the
domain of the function.
 3
if x  2
 2 x  1,

f ( x)   x  1,
if  2  x  1
 3,
if x  1


Exercise 2
Evaluate g(x) at the values below.
2 x  1, if x  1
g ( x)  
3x  1, if x  1
1.
2.
3.
g(1)
g(5)
g(−3)
Exercise 3
Graph g(x).
2 x  1, if x  1
g ( x)  
3x  1, if x  1
Graphing Piecewise Functions
Method 1:
1. Rather than starting at
the 𝑦-intercept, start at
the domain’s breaking
point. Use the slope to
graph the partial line in
the correct direction.
2. Repeat for each piece
of your function.
Graphing Piecewise Functions
Method 2:
1. Graph one of the equations
in the piecewise function as
you normally would.
2. Erase the part of the graph
that you don’t need
according to the domain of
the piece.
3. Repeat for each piece of
your function.
Exercise 4
−12𝑥 − 6, 𝑥 ≤ −4
Graph 𝑓 𝑥 =
𝑥 + 5,
𝑥 > −4
Exercise 4
Write a piecewise
function for the
graph shown.
4-1: Intro to Piecewise-Defined Functions
Objectives:
1. To evaluate, write,
and graph piecewise
functions
Assignment:
• P. 60: 14-17
• P. 71: 1-9
• Challenge Problems