section 4.2 - functions. answer the following for each question: does the information given...
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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
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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,