Algebra II 1

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) 5. f(3) 6. f(4a)

Evaluating, Graphing, and Writing Piecewise Functions

Algebra II

A combination of equations each corresponding to a given domain.

Algebra II 3

Evaluate each.

1. f(3)

2. f(-4)

3. f(1)

= (3) + 4 = 7

= 2(-4)2 – 2 = 2(16) – 2 = 30

= (1) + 4 = 5

2x2 – 2 if x < 1 x + 4 if x ≥ 1

f(x)= {

Algebra II 4

= (-3) − 1 = -4

= (-1) − 1 = -2

= ((2) – 3)2 = (-1)2 = 1

x − 1 if x ≤ -1(x − 3)2 if x > -1f(x)= {

Evaluate each.

1. f(-3)

2. f(-1)

3. f(2)

Algebra II 5

= 4

= 2(5)2 – 3 = 2(25) – 3 = 47

= 3(-8) – 2 = -24 – 2 = -26

Evaluate each.

1. g(5)

2. g(-2)

3. g(-8)

3x – 2 if x < -34 if -3 ≤ x < 52x2 – 3 if x ≥ 5

g(x)= {

Algebra II 6

7Algebra II

x + 3 if x < ½2x – 1 if x ≥ ½g(x)= {

2x if x < -2x – 2 if -2 ≤ x < 22x2 + 1 if x ≥ 2

f(x)= { Evaluate each piecewise function for the given values.

1. f(½)

2. f(2)

3. f(-5)

4. g(½)

5. g(0)

6. g(-1)

-3/2

9

-10

0

3

2

x – 3 if x < 2-½x + 1 if x ≥ 2

f(x)=

{ x – 3 if x < 2-½x + 1 if x ≥ 2

Graph thepiecewise function:

Algebra II 8

3x + 1 if x ≤ -1x + 2 if x > -1

f(x)=

{ 3x + 1 if x ≤ -1x + 2 if x > -1

Graph thepiecewise function:

Algebra II 9

-2x if x < -2⅔x – 1 if x ≥ -2

f(x)=

{ -2x if x < -2⅔x – 1 if x ≥ -2

Graph thepiecewise function:

Algebra II 10

-3 if x < 0-x – 1 if x ≥ 0

f(x)=

{ -3 if x < 0-x – 1 if x ≥ 0

Graph thepiecewise function:

Algebra II 11

2x – 1 if x < -23 if -2 ≤ x ≤ 2-¼x if x > 2

f(x)=

{ 2x – 1 if x < -23 if -2 ≤ x ≤ 2-¼x if x > 2

Graph thepiecewise function:

Algebra II 12

Evaluate each given the piece-wise function:

1.f(-2)2.f(6)3.f(-5)

Algebra II 13

4x2 + 5 if x < -33x – 2 if -3 ≤ x < 5–3 if x ≥ 5

f(x)= {

4. Graph:

f(x)=

{

1/3x + 1 if x < -33x if -3 ≤ x < 22 if x > 2

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

(3 – 1) = -2 = -2(-3 + 2) 1

y – 1 = -2(x + 2)y = 2x – 3

(-5 + 4) = -1 (2 + 1) 3y + 4 = -⅓(x + 1)

y = -⅓x – 13/3

Write the piecewisefunction that is graphed.

Algebra II 15

(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

Write the piecewisefunction that is graphed.

Algebra II 16

(2 – 0) = 2 = 2 (1 – 0) 1

y – 0 = 2(x + 0)y = 2x

(2 + 1) = 3 = -1 (-3 - 0) -3y + 1 = -1(x + 0)

y = -x – 1

Write the piecewisefunction that is graphed.

Algebra II 17

(5 – 3) = 2 = 1 (-3 + 5) 2

y – 5 = 1(x + 3)y = x + 8 Slope is 0

horizontal line

y = 3

Write the piecewisefunction that is graphed.

(1 – 0) = 1 = -½ (1 – 3) -2

y – 0 = -½(x – 3)y = -½x + 3/2

Algebra II 18

1. Graph the piece-wise function:

2. Write a piece-wise function for this graph:

Algebra II 19

x + 8 if x < -3 3 if -3 ≤ x < 1-½x + 3/2 if x ≥ 1

f(x) =

{