1. Bellwork: Graph each line: 1. 3x – y = 6 2. Y = -1/2 x + 3 Y = -2
If f(x) = 3x2 – 9, find each.
4. f(-2) f(3) f(4a)
Algebra II

2. Evaluating, Graphing, and Writing Piecewise Functions
Algebra II

3. Piecewise Functions
A combination of equations each corresponding to a given domain.
Algebra II

4. Example 1 f(x)= { 2x2 – 2 if x < 1 x + 4 if x ≥ 1 Evaluate each.
= (3) + 4 = 7
= 2(-4)2 – 2 = 2(16) – 2 = 30
= (1) + 4 = 5
Algebra II

5. Example 2 x − 1 if x ≤ -1 f(x)= { (x − 3)2 if x > -1 Evaluate each.
= (-3) − 1 = -4
= (-1) − 1 = -2
= ((2) – 3)2 = (-1)2 = 1
Algebra II

6. Example 3 g(x)= { 3x – 2 if x < -3 4 if -3 ≤ x < 5
Evaluate each.
1. g(5)
2. g(-2)
3. g(-8)
= 2(5)2 – 3 = 2(25) – 3 = 47
= 4
= 3(-8) – 2 = -24 – 2 = -26
Algebra II

7. Find each. f(½) f(2) f(-5) -3/2 9 -10 4. g(½) 5. g(0) 6. g(-1) 3 2
2x if x < -2
x – if -2 ≤ x < 2
2x if x ≥ 2
f(x)= {
x + 3 if x < ½
2x – 1 if x ≥ ½
g(x)= {
Evaluate each piecewise function for the given values.
f(½)
f(2)
f(-5)
-3/2 9
-10
4. g(½)
5. g(0)
6. g(-1) 3 2
Algebra II

8. Graphing: Example 1 f(x)= { x – 3 if x < 2 -½x + 1 if x ≥ 2
Graph the
piecewise function:
f(x)= {
x – 3 if x < 2
-½x + 1 if x ≥ 2
x – 3 if x < 2
-½x + 1 if x ≥ 2
Algebra II

9. Graphing: Example 2 f(x)= { 3x + 1 if x ≤ -1 x + 2 if x > -1
Graph the
piecewise function:
f(x)= {
3x + 1 if x ≤ -1
x + 2 if x > -1
3x + 1 if x ≤ -1
x + 2 if x > -1
Algebra II

10. Graphing: Example 3 f(x)= { -2x if x < -2 ⅔x – 1 if x ≥ -2
Graph the
piecewise function:
f(x)= {
-2x if x < -2
⅔x – 1 if x ≥ -2
-2x if x < -2
⅔x – 1 if x ≥ -2
Algebra II

11. Graphing: Example 4 f(x)= { -3 if x < 0 -x – 1 if x ≥ 0
Graph the
piecewise function:
f(x)= {
if x < 0
-x – 1 if x ≥ 0
if x < 0
-x – 1 if x ≥ 0
Algebra II

12. Graphing: Example 5 f(x)= { Graph the piecewise function:
2x – 1 if x < -2
if -2 ≤ x ≤ 2
-¼x if x > 2
2x – 1 if x < -2
if -2 ≤ x ≤ 2
-¼x if x > 2
Algebra II

13. Find each. Graph: Evaluate each given the piece-wise function: f(x)={
1/3x + 1 if x < -3
3x if -3 ≤ x < 2
if x > 2
4x if x < -3
3x – 2 if -3 ≤ x < 5
– if x ≥ 5
f(x)= {
Algebra II

14. Writing a Piecewise Function
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

15. function that is graphed.
Example 1
Write the piecewise
function that is graphed.
(3 – 1) = -2 = -2
(-3 + 2)
y – 1 = -2(x + 2)
y = 2x – 3
(-5 + 4) = -1
(2 + 1)
y + 4 = -⅓(x + 1)
y = -⅓x – 13/3
f(x) = {
2x – 3 if x ≤ -1
-⅓x – 13/3 if x > -1
Algebra II

16. function that is graphed.
Example 2
Write the piecewise
function that is graphed.
(6 – 5) = 1
(1 + 4)
y – 6 = ⅕(x – 1)
y = ⅕x + 29/5
(0 + 1) = 1 = 1
(3 – 2)
y – 0 = 1(x + 3)
y = x – 3
f(x) = {
⅕x + 29/5 if x < 1
x – 3 if x ≥ 1
Algebra II

17. function that is graphed.
Example 3
Write the piecewise
function that is graphed.
(2 + 1) = 3 = -1
(-3 - 0)
y + 1 = -1(x + 0)
y = -x – 1
(2 – 0) = 2 = 2
(1 – 0)
y – 0 = 2(x + 0)
y = 2x
f(x) = {
-x – 1 if x ≤ 0
2x if x > 0
Algebra II

18. function that is graphed.
Example 4
Write the piecewise
function that is graphed.
(5 – 3) = 2 = 1
(-3 + 5)
y – 5 = 1(x + 3)
y = x + 8
Slope is 0
horizontal line
(1 – 0) = 1 = -½
(1 – 3)
y = 3
y – 0 = -½(x – 3)
y = -½x + 3/2
f(x) = {
x + 8 if x < -3
if -3 ≤ x < 1
-½x + 3/2 if x ≥ 1
Algebra II

19. Closure: Graph the piece-wise function:
Write a piece-wise function for this graph:
f(x) = {
x + 8 if x < -3
if -3 ≤ x < 1
-½x + 3/2 if x ≥ 1
Algebra II