Section 4.2 - Functions

Answer the following for each question:•Does the information given constitute a function?•If not, briefly justify your answer.

JanuaryFebruaryMarchJuly

WinterSpringSummer

t 0 1 2 3f(t) 5 2 2 4

2y x 6x 4 2x y

YES YES

YES NoIf x = 1, y = 1 and –1

FordBushCarterClinton

PresidentVice-President

NoFord is mapped to both

President and Vice-President

2, 4 , 3, 4 , 1, 5

YES

6, 5 , 8, 1 , 6, 3

No6 is mapped to both 5 and 3

x y 7

YES

2x y 4

No0 is mapped to both 2 and -2

2 2x y 16

No0 is mapped to both 4 and -4

f x 7x 3

f 1 7 31

f 1 4

2f x 2x 3x 4

2f 31 2 41 1

f 11

f x 2x 7

f 2x 1 x 71

xx 51f 2

2f x x 2x

2x 1 x 1 2 1f x

2x 2 1 x 2x 2f x1

2x 11f x

f x 4x 9

f 4x 92 2x

f 2x 8x 9

6x 3f x

2x 1

55

6

1

5 3f

2

33 11

9f 5

3

Given the function f x 8 3x, evaluate :

f 2

f

f 2 x

8 23 2

88 3 3

2 x 2 3x8 3

2x 3Given the function f x , evaluate :

5 xf 1

f 2x

f x 3

2 31 1

15 6

2x

2x

2 3 3

5 x5

4x

2

2 3

5

x 3

x

2x

8 x3

3

t 0 1 2 3 4 5 6f(t) 5 2 2 4 7 1 -2g(t) 2 3 5 1 3 -2 5

f 2

g 6

2g 4 3g 2

2f 3

3f 2 4g 1

g 2 f 3

f 6 f 3

g 0 f 5

2

5

2 3 3 5 9

24 16

3 2 4 3 6

5 4 20

2 4 6

2 1 3

Evaluating Functions on Calculator

New Menu

2Given the function f x 2x 3x 4, evaluate :

f 2.3

f 7.1 f 0.5

7x 2Given the function f x , evaluate :

2x 3f 6.1

f 3.7

f 1.4

Domain – All elements substituted (x)Range – All answers (y)

Find the domain and range of each of the following functions:

JanuaryFebruaryMarchJuly

WinterSpringSummer

Domain: January, February, March, JulyRange: Winter, Spring Summer

t 0 1 2 3f(t) 5 2 2 4

Domain: 0, 1, 2, 3Range: 5, 2, 4

6, 5 , 8, 1 , 6, 3 Domain: 6, 8Range: 5, -1, 3

x y 7 Domain: Range:

, ,

Find the domain of each of the following functions:

2g x x 2x

,

f x2

1

x

, 2 , 2,

x 5

6x

xf

2

, 3 , 3,

f x 3x 6

x

x

2

3 6 0

2,

x 2 x

x2 x 4

4h

x

, 4 , 4, 2 , 2,

x

x2x

7g

5

0 0

5x

2x 5 x 7

x 72

5,

2

Find the domain of each of the following functions:

6f x

2x 3

2

2

x 5x 6g x

x 6x 8

h x 6

f x 3 2x 3

4g x

x 1

x 1

h x2x 8

2f x 2x 3x 1 g x 3 x 9 1 2h x

x 2 x 3

3 3, , ,2 2

, 2 , 2, 4 , 4, ,

3,2

,1 , 1, 1, 4 , 4,

, 9, , 3 , 3, 2 , 2,