14.1 Graphing Functions and Relations

Common Functions
Parent Function
y=x

Family
linear

y = x2
y = x3
y = |x|

quadrat...
Linear Function
y=x
x

y=x

y

-2

-2

-1

-1

0

0

1

1

2

2

3

3
Quadratic Function

y=
x

y = x2

y

-2

4

-1

1

0

0

1

1

2

4

3

9

2
x
Cubic Function

y=
x

y = x3

y

-2

-8

-1

-1

0

0

1

1

2

8

3

27

3
x
Absolute Value Function
y = |x|
x

y = |x|

y

-2

2

-1

1

0

0

1

1

2

2

3

3
Square Root Function
y = √x
x

y= x

y

1

1

4

2

9

3

16

4

25

5

36

6
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
Linear Function
y=x+2
x
-2
-1
0
1
2
3

y=x

y
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...
Am I Linear???
Now plot the data to see how it looks graphically

y

non-linear function
Area of Table Top

linear functio...
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 ...
Unit Rate of Change
Your cell phone plan includes 400
anytime minutes. What is the per minute
charge after 400 minutes are...
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Linear nonlinearfunctionsedmodo 2013-2014

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  • Print the next 8 slides 4 to a page and let the students work with the tables and graphs, then use the powerpoint to review their work.
  • Discuss the characteristics that give the function its shape—constant rate of change.
  • Discuss the characteristics that give the function its shape—an input and its opposite both have the same output.
  • Discuss the characteristics that give the function its shape—an input and its opposite have opposite outputs
  • Discuss the characteristics that give the function its shape—an input and its opposite have the same ouput.
  • Discuss the characteristics that give the function its shape—as inputs get much higher, outputs remain low.
  • Explain that any integer divided by zero is undefined—students have trouble with this concept; you can’t have a part of nothing.
  • Discuss the characteristics that give the function its shape—constant rate of change, but does not cross the origin.
  • Discuss rate of change and difference between consecutive terms for both tables
  • Discuss the characteristics that give the function its shape—constant rate of change, but does not cross the origin.
  • Discuss the characteristics that give the function its shape—constant rate of change, but does not cross the origin.
  • Linear nonlinearfunctionsedmodo 2013-2014

    1. 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. 2. Linear Function y=x x y=x y -2 -2 -1 -1 0 0 1 1 2 2 3 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. 4. Cubic Function y= x y = x3 y -2 -8 -1 -1 0 0 1 1 2 8 3 27 3 x
    5. 5. Absolute Value Function y = |x| x y = |x| y -2 2 -1 1 0 0 1 1 2 2 3 3
    6. 6. Square Root Function y = √x x y= x y 1 1 4 2 9 3 16 4 25 5 36 6
    7. 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. 8. Linear Function y=x+2 x -2 -1 0 1 2 3 y=x y
    9. 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. 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. 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. 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

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