Pre Calc – Graphing Properties
Write the domain and range of each relation below in interval notation.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
For each relation, choose the correct answer.
16)
17)
18)
X
5
2
4
-3
Y
5
-3
0
2
Domain
Range
Ordered Pairs
Inverse
Is a function?
Domain
Range
Ordered Pairs:
Inverse:
Is a function?
Domain
Range
Ordered Pairs:
Inverse:
Is a function?
a)
b)
c)
d)
e)
{ ( 5, 5 ), ( 2, -3 ), ( 4, 0 ), ( -3, 2 ) }
{ ( 5, 5 ), ( -3, 2 ), ( 0, 4 ), ( 2, -3 ) }
{ 5, -3, 0, 2 }
{ 5, 2, 4, -3 }
{ ( 5, 2 ), ( 4, -3 ), ( 5, -3 ), ( 0, 2 ) }
a)
b)
c)
d)
e)
a)
b)
c)
d)
e)
{
{
{
{
{
( -2, -2 ), ( 2, -1 ), ( 3, 0 ), ( 5, 3 ) }
( -2, -2 ), ( -1, -2 ), ( -1, 2 ), ( 0, 3 ), ( 3, 5 ), ( 4, 5 ) }
-2, 2, 3, 5 }
-2, -1, 0, 3, 4 }
( -2, -2 ), ( -2, -1 ), ( 2, -1 ), ( 3, 0 ), ( 5, 3 ), ( 5, 4 ) }
{ -3, -2, 0, 2 }
{ ( -3, 1 ), ( -2, -2 ), ( 0, -2 ), ( 2, 3 ) }
{ ( 1, -3 ), ( -2, -2 ), ( -2, 0 ), ( 3, 2 ) }
{ 3, 2, 0, 2 }
{ 1, -2, 3 }
Match the graphs with the matching equations (Note that x and y scales may be unequal)
19)
y=x–5
20)
-3x + 4 = y
21)
5=y
22)
y = -4x – 5
23)
y=x+6
24)
y=
a)
b)
c)
x
2
!
d)
e)
f)
Use the graph of y = f(x) to match the function with its graph.
25)
y = f(x + 5 )
26)
y = f(x) – 5
27)
y = -f(-x) – 2
28)
y = -f(x – 4)
29)
y = f(x + 6 ) + 2
30)
y = f(x – 1) + 3
Use the vertical line test to determine if the following graphs are functions.
31)
35)
32)
33)
36)
34)
37)
38)
39)
40)
41)
42)
43)
Determine if the functions are odd, even, or neither.
44)
f(x) = 4 – x2
47)
f(x) = x + 2
51)
The graphs of f, g,
and h are shown
to the right,
determine
whether each
function is odd,
even, or neither.
45)
48)
f(x) = x ( 4 – x2 )
f(x) = 4x2 + 2
49)
52)
46)
f (x) =
f(x) = 4x – x2
1
x "1
50)
f (x) =
1
x2 " 1
The domain of the function
f show to the right is
!
-6 ≤ x ≤ 6.
!
a)
b)
Complete the graph of
f given that f is even.
Complete the graph of
f given that f is odd.
Find the domain and range of each function.
53)
f(x) = 4 – x
57)
f (x) =
54)
4x
f (x) = 25 " x 2
58)
2
6x + 13x " 5
!
f (x) =
55)
56)
f (x) = x " 1
4x " 3
59)
2
x "4
!
f(x) = | x – 2 |
f(x) = 9 – x2
Determine the symmetry of each graph [ x-axis / y-axis / origin ].
!
60)
x2
=5
61)
!
y = x3
64)
y = 2 3"x
65)
y = 1 " x2
+
y2
3
Find the points of intersection Algebraically.
69) x2 + y2 = !
25
! 68) x + y = 2
!
2x – y = 1
y = -2x + 10
62)
63)
x = y2 + 4
y=
1
1 + x2
3
676) y = 4 " x 2
67)
y = x2
!
70)
y=x–1
!
x = 3 – y2
71)
Use
a)
b)
c)
d)
e)
the graph of f and g to answer the following:
Identify the domains and ranges of f and g.
Identify f(-2) and g(3).
For what values of x is f(x) = g(x)?
Estimate the solution(s) of f(x) = 2
Estimate the solutions of g(x) = 0
72)
Use
a)
b)
c)
d)
e)
the graph of f and g to answer the following:
Identify the domains and ranges of f and g.
Identify f(-2) and g(3).
For what values of x is f(x) = g(x)?
Estimate the solution(s) of f(x) = 2
Estimate the solutions of g(x) = 0
Also – Section 1.2 in your book: Problems 37 – 46, 59 – 62, 63.