1. 14.1 Graphing Functions and Relations
Common Functions
Parent Function
y=x
Family
linear
y = x2
y = x3
y = |x|
quadratic
cubic
absolute value
y = x
square root
1
y= x
rational

2. Linear Function
y=x
x
y=x
y
-2
-2
-1
-1
0
0
1
1
2
2
3
3

3. Quadratic Function
y=
x
y = x2
y
-2
4
-1
1
0
0
1
1
2
4
3
9
2
x

4. Cubic Function
y=
x
y = x3
y
-2
-8
-1
-1
0
0
1
1
2
8
3
27
3
x

5. Absolute Value Function
y = |x|
x
y = |x|
y
-2
2
-1
1
0
0
1
1
2
2
3
3

6. Square Root Function
y = √x
x
y= x
y
1
1
4
2
9
3
16
4
25
5
36
6

7. x
-4
-2
y=
Rational Function
1
y=
x
1
x
y
1
4
1

2

-1
-1
0
Undefined
1
1
2
1
2
1
4
4

8. Linear Function
y=x+2
x
-2
-1
0
1
2
3
y=x
y

9. Am I Linear???
A company builds square table tops with sides in 5 different lengths from 1
foot to 5 feet. They also put a decorative border around the sides of the
tables. Use the functions below to determine the area and perimeter of the
tables so the company will know how much material is needed for each table.
Are the functions linear? Explain your reasoning.
non-linear function
linear function
s(ft)
s2
A(ft2)
s(ft)
4s
P(ft)
1
12
1
1
4(1)
4
2
22
4
2
4(2)
8
3
32
9
3
4(3)
12
4
42
16
4
4(4)
16
5
52
25
5
4(5)
20

10. Am I Linear???
Now plot the data to see how it looks graphically
y
non-linear function
Area of Table Top
linear function
Perimeter of Table Top
y
24
24
20
20
16
Area (ft2)
12
16
Perimeter(ft)
12
8
8
4
4
0
x
1
2
3
4
Side Length (ft)
5
6
0
x
2
3
4
Side Length (ft)
5
6

11. Am I Linear???
Now lets compare area and perimeter of one side of
a cube-shaped box with the boxes volume.
y
Area of Box Side
y
Perimeter of Box Side
y
24
24
72
20
20
60
16
Area
(ft2) 12
16
Perimeter(ft)
12
48
Volume
(ft3) 36
8
8
24
4
4
Volume of Box
12
0
1
2
3
x
4
5
Side Length (ft)
s(ft)
s2
A(ft2)
1
12
1
2
22
4
3
32
9
4
42
5
52
6
0
1
2
3
x
4
5
6
0
1
2
3
x
4
5
Side Length (ft)
Side Length (ft)
s(ft)
s3
A(ft3)
1
13
1
2
22
8
3
33
27
16
4
43
64
20
5
53
125
s(ft)
4s
P(ft)
1
4(1)
4
2
4(2)
8
3
4(3)
12
16
4
4(4)
25
5
4(5)
6

12. Unit Rate of Change
Your cell phone plan includes 400
anytime minutes. What is the per minute
charge after 400 minutes are used?
Which plant is growing faster?
Phone cost
Plant Growth
6
100
5
Height (in.)
Monthly Cost ($)
120
80
60
40
4
3
2
20
1
0
200
400
Talk time (min)
Rate for talk time over
400 minutes:
600
0
1
2
3
4
Time (weeks)
Plant A:
Plant B:
5
6