1.2--Functions and Their Properties
Determine whether or not each relation is a function:
1)
2)
3)
4)
Find the domain & range
for each function:
5)
y = 5
6)
y =
7)
y =
x - 10
x-3
x+4
x + 8
DOMAIN
RANGE
1.2--Functions and Their Properties
Find the domain & range
for each function:
y =
9)
y = cos2x + 10
y =
RANGE
3
2x + 5
8)
10)
DOMAIN
3x2 - 6x - 240
x2 - 11x + 10
3 types of discontinuity:
point
jump
infinite
1.2--Functions and Their Properties
Find any points of discontinuity. Tell which type of
discontinuity it is (point, jump, or infinite):
11)
13)
3
x-2
y =
y =
[x ]
12)
14)
y =
y =
x2 - 3x - 18
2x + 6
x2 - 9x + 20
x2 - 4x
Find the x-values (if any) at which f(x) is not continuous.
State whether the discontinuity is removable or not:
15)
16)
f(x) =
f(x) =
2x + 8
x + 4
5x - 8 , x ≤ 4
x
x2 - 13 , x > 4
1.2--Functions and Their Properties
17)
Find the value of k that will make the function continuous:
5x - 2
4
f(x) =
3x2 + 11
3k - 13
, x ≤ 6
, x > 6
Decide whether each point is an absolute max/min,
a relative max/min, or neither:
G
D
B
I
F
I
H
C
A
E
J
L
1.2--Functions and Their Properties
increasing
concave up
decreasing
concave down
decreasing
concave up
increasing
concave down
A point of inflection is where the concavity changes.
18)
Find the intervals where the function is increasing
or decreasing, and concave up or concave down.
Use interval notation:
y
10
5
­10
­5
5
­5
­10
10
x
1.2--Functions and Their Properties
EVEN functions have y-axis symmetry.
ODD functions have origin symmetry.
Tell whether the function is EVEN, ODD, or NEITHER:
19)
y = x5 - 6x3
21)
y =
x2
x-1
23)
y =
8x2
x2 + 1
20)
y = x4 + 2x3
x5
22)
y =
24)
y = sin x
x2 - 6
1.2--Functions and Their Properties
Tell whether the function is EVEN, ODD, or NEITHER:
25)
y = cos x
26)
y = tan x
27)
y = sin2x
28)
y = cos3x
Find all horizontal and vertical asymptotes, then describe
the end behavior of each graph:
29)
y =
31)
y =
2x + 5
6x - 12
2x + 6
x2 - 17x - 60
30)
32)
y =
y =
18x3 - 3x
9x2 + 4
3x4 + 21x3
x2 + 11x + 28