Graph each line:
1. 3x – y = 6
2. Y = -1/2 x + 3
3.  Y = -2
If f(x) = 3x2 – 9, find each. 4. f(-2) Algebra II
5. f(3) 6. f(4a)
1
Evaluating and
Graphing Piecewise
Functions
Algebra II
¡  A
combination of equations
each corresponding to a given
domain. Algebra II
3
f(x)=
{
2x2 – 2
x+4 if x < 1
if x ≥ 1
Evaluate each. 1. f(3)
= (3) + 4 = 7
2. f(-4) = 2(-4)2 – 2 = 2(16) – 2 = 30
3. f(1)
Algebra II
= (1) + 4 = 5
4
f(x)=
{
x − 1 if x ≤ -1
(x − 3)2 if x > -1
Evaluate each. 1. f(-3) = (-3) − 1 = -4
2. f(-1) = (-1) − 1 = -2
3. f(2)
Algebra II
= ((2) – 3)2 = (-1)2 = 1
5
g(x)=
{
3x – 2 if x < -3
4 if -3 ≤ x < 5
2x2 – 3 if x ≥ 5
Evaluate each. 1. g(5)
= 2(5)2 – 3 = 2(25) – 3 = 47
2. g(-2) = 4
3. g(-8) = 3(-8) – 2 = -24 – 2 = -26
Algebra II
6
f(x)=
{
2x
if x < -2
x–2
if -2 ≤ x < 2
2x2 + 1 if x ≥ 2
g(x)=
{
x+3
2x – 1
if x < ½
if x ≥ ½
Evaluate each piecewise function for the given values.
1.  f(½)
-3/2
4. g(½)
0
2.  f(2)
9
5. g(0)
3
3.  f(-5)
-10
6. g(-1)
2
Algebra II
7
Graph the
piecewise function:
f(x)=
{
x – 3 if x < 2
+ 1 if x ≥ 2
-½x
Algebra II
8
Graph the
piecewise function:
f(x)=
{
3x + 1 i f x ≤ -1
x + 2 i f x > -1
Algebra II
9
Graph the
piecewise function:
f(x)=
{
-2x i f x < -2
– 1 i f x ≥ -2
⅔x
Algebra II
10
Graph the
piecewise function:
f(x)=
{
-3 if x < 0
– 1 if x ≥ 0
-x
Algebra II
11
Graph the
piecewise function:
f(x)=
{
2x – 1 if x < -2
3
if -2 ≤ x ≤ 2
-¼x if x > 2 Algebra II
12
Evaluate each
given the piecewise function:
{
f(x)=
1. 
2. 
3. 
Graph: {
f(x)=
4x2 + 5 if x < -3
3x – 2 if -3 ≤ x < 5
–3 if x ≥ 5
f(-2)
f(6)
f(-5) Algebra II
4. 
1/3x + 1 if x < -3
3x
if -3 ≤ x < 2
2
if x > 2
13
¡  Write
the equation for each
piece of the function
¡  Write
the domain for each
piece of the function
§  use inequality notation to represent
the domain in each piece
Algebra II
14
Write the piecewise
function that is graphed.
(3 – 1) = -2 = -2
(-3 + 2)
1
y – 1 = -2(x + 2)
y = 2x – 3
(-5 + 4) = -1 (2 + 1)
3
y + 4 = -⅓(x + 1)
y = -⅓x – 13/3
f(x) =
Algebra II
{
2x – 3
if x ≤ -1
-⅓x – 13/3 if x > -1
15
Write the piecewise
function that is graphed.
(6 – 5) = 1 (1 + 4)
5
y – 6 = ⅕(x – 1)
y = ⅕x + 29/5
(0 + 1) = 1 = 1
(3 – 2)
1
y – 0 = 1(x + 3)
y = x – 3
f(x) =
Algebra II
{
⅕x + 29/5 if x < 1
x – 3
if x ≥ 1
16
Write the piecewise
function that is graphed.
(2 + 1) = 3 = -1
(-3 - 0)
-3
y + 1 = -1(x + 0)
y = -x – 1
(2 – 0) = 2 = 2
(1 – 0)
1
y – 0 = 2(x + 0)
y = 2x
f(x) =
Algebra II
{
-x – 1 if x ≤ 0
2x if x > 0
17
Write the piecewise
function that is graphed.
(5 – 3) = 2 = 1
(-3 + 5)
2
y – 5 = 1(x + 3)
y=x+8
(1 – 0) = 1 = -½
(1 – 3) -2
Slope is 0
horizontal line
y = 3
y – 0 = -½(x – 3)
y = -½x + 3/2
f(x) =
Algebra II
{
x+8
if x < -3
3 if -3 ≤ x < 1
-½x + 3/2 if x ≥ 1
18
1. 
Graph the piece-wise function: f(x) =
2. 
{
x+8
if x < -3
3 if -3 ≤ x < 1
-½x + 3/2 if x ≥ 1
Write a piece-wise
function for this
graph: Algebra II
19