HW 1 – 1 : Functions Review!
Name _______________________
Determine the domain and range for each relation and state if the relation is a function.
1. ( 2 , 3 ) ( 3 , 2 ) ( –2 , 2 ) ( 0 , 3 )!
2.
(1 , 5 ) ( 2 , 3 ) ( 3 , 5 ) ( 2 , 7)
Domain =! {
}!
Domain =! {
}
Range = ! {
}!
Range = !{
}
Function? _____!
Function? _____
3.!
4.
!
!
Domain = {
}!
Range = ! {
}!
Function? _____!
Domain =! {
}
Range = !{
}
Function? _____
5. List the letters of each relation that is NOT a Function.!
A.
!
5.______________
B.!
C.
2
4
1
4
2
4
3
2
3
0
2
3
2
5
–2
5
5
!
D. !
E.
!
–2
4
3
!
6
2
5
8
F.
–5
–5
–1
–1
2
2
7
!
Math 400 HW 1– 1
!
7
–2
6
8
!
!
Page 1 of 10!
© 2016 Eitel
6. List the letters of each relation that is NOT a Function.
A. !
B.!
!
y
C.!
y
x
y
x
x
!
!
!
D. !
y
E.!
y
x
F.
y
x
!
!
6. _________________
x
!
G !
H.!
!
!
7. List the letters of each relation that is NOT a Function.!
A. y = 2x − 3!
B. y = x 2 − 3!
!
!
F. y = 5!
K. x 2 + y 2 = 1!
I.
!
7. ___________________
C. y = x !
D. x = 4 !
E y=3 x
G. y < 3x − 5!
H. 9 = 2x 2 − 3y !
I. x = 2y 2 − 3!
J. x = y
L. y = x 3 !
M. 9x 2 + 4 y 2 = 36!
N. x = y 3 !
O. y = x
!
!
Math 400 HW 1– 1
!
Page 2 of 10!
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Domain Restrictions
There are several common domain issues we encounter with functions in this class.
A. f (x) =
g(x)
h(x)
f (x) has a domain restriction at all the x values where the denominator is
equal to 0. The domain for f (x) is all real x values except the x values
where h(x) = 0
B. f (x) = g(x)
The square root function requires that the values under the square root must be
greater than or equal to 0. The domain for f (x) is all real x values where
g(x) ≥ 0
C.
f (x) = log b ( g(x))
The log function requires that the values for g(x) must be greater than 0.
The domain for f (x) is all real x values where g(x) > 0
State the domain for each function:
8.
x+3
f (x) = 3
!
x − 9x
9. f (x) =
Domain:
2x + 3
Domain:
2
6x − 5x − 12
10. f (x) = −5x + 10
Math 400 HW 1– 1
{ x ∈ Reals | ________________________ }
{ x ∈ Reals | ________________________ }
!
Domain:
!
{ x ∈ Reals | ________________________ }
Page 3 of 10!
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11. f (x) =
x−2
x − 10
!
Domain:
{ x ∈ Reals | ________________________ }
12. f (x) = log 2 (−3x + 9)
Domain:
{ x ∈ Reals | ________________________ }
13. f (x) =
log 5 (x + 4)
log 5 (2x − 6)
Domain:
{ x ∈ Reals | ________________________ }
14. f (x) =
log 3 (x + 4)
x−2
Math 400 HW 1– 1
!Domain:
{ x ∈ Reals | ________________________ }
!
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Function Notation
f (x) = 3x 3 − x 2
g(x) = 2x −1
h(x) = 5 − 4 x
m(x) =
3
x −5
k(x) = x − 3
Evaluate the following given the functions above.
15. f (2) !
16. g
⎛ 5⎞
⎝ 2⎠
19. m (k (7)) !
20.
⎛ ⎛ 1 ⎞⎞
f ⎜h
⎟!
⎝ ⎝ 2 ⎠⎠
!
17. k (15) !
18. g (h (2))
21. k (g ( f (1))) !
22. g (g (g (1)))
23. Let f (x) = 4 x 2 − 2x + 1 and g(x) = −2x 2 + 7x − 9 Find the following:
A.
( f + g)(x)!
B.
C. Domain of ( f + g)(x) ______________!
( f + g)(1) !
!
!
24. Let f (x) = 4 x 2 − 2x + 1 and g(x) = −2x 2 + 7x − 9 Find the following:
A. ( f − g)(x) !
B.
( f − d)(3) !
C. Domain of ( f − g)(x) ______________!
Math 400 HW 1– 1
!
Page 5 of 10!
© 2016 Eitel
25. Let f (x) = 4 x + 2 and g(x) = 3x 2 − 1 and h(x) = 2x − 5 Find the following:
A.
( f g)(x)!
B.
Domain of
C.
( f g)(x) ______________!
26. Let f (x) = 2x + 5 and g(x) = 25 − 4 x 2
.
⎛ f⎞
A.
⎜ ⎟ (x)!
⎝ g⎠
B.
⎛ f⎞
Domain of ⎜ ⎟ (x) ______________!
⎝ g⎠
(h f )(x)
!
D. Domain of (h f )(x) ______________
Find the following:
B.
⎛ g⎞
⎜ ⎟ (x)
⎝ f⎠
!
⎛ g⎞
D. Domain of ⎜ ⎟ (x) ______________
⎝ f⎠
27. Let f (x) = 18x 2 + 21x − 4 and g(x) = 6x −1 Find the following:
A.
B.
⎛ f⎞
⎜ ⎟ (x)!
⎝ g⎠
C.
⎛ f⎞
Domain of ⎜ ⎟ (x) ______________!
⎝ g⎠
Math 400 HW 1– 1
!
⎛ g⎞
⎜ ⎟ (x) !
⎝ f⎠
⎛ g⎞
D. Domain of ⎜ ⎟ (x) ______________
⎝ f⎠
Page 6 of 10!
© 2016 Eitel
28. If f (x) = 2x − 5 and g(x) = − x 2 + 2 then find the following
A.
g( f (x) )!
C.
f ( f (x) ) !
B.
f ( g(x) ) !
D. g( g(x) )
29. Let f (x) = x 3 − 2 and g(x) = 3 x + 2 Find the following
A.
B.
g( f (x))!
Math 400 HW 1– 1
!
f ( g(x) ) !
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© 2016 Eitel
30. State if the graph shown is even, odd or neither.
Even functions: _____________!
Odd functions: _____________
Neither: _____________
A.!
B.!
C.
!
!
D.!
!
!
E.!
F.
( 1, 3 )
!
G.!
!
!
H.!
I.
!
J.!
!
!
K.!
L.
( –2 , 3 )
!
Math 400 HW 1– 1
!
!
Page 8 of 10!
© 2016 Eitel
Show the work required to PROVE that the functions below are even, odd or neither.
31. f (x) = x 2 + 1
32. f (x) = x 3 + x
x
33. f (x) = 2
x −1
34. f (x) = x 3 + 5
Math 400 HW 1– 1
!
Page 9 of 10!
© 2016 Eitel
Find the equation of the line that contains the two given points in
35. (−1, − 4 ) and
(−5,4) !
!
36
( y − y1) = m ( x − x1) form.
(4, − 4) and (−1,−3)
Find the equation of the line that contains the two given points in y = m x + b form.
37.
(2, 2) and (−4,−1) !
39. (−1, − 3) and
Math 400 HW 1– 1
(−5,−3) !
!
!
38. (6, 1) and
(−3,−2)
!
40. (4,−2) and
(4,−1)
Page 10 of 10!
© 2016 Eitel