1. 8.6.2 Representations of Functions

2. Vocabulary
Function Rule – An equation that describes how inputs and outputs affect one another.
Example: I have to add 1 cup of sugar for every 2 gallons of water I use to make iced tea.
Function Rule:
s = 1/2w
w = 2s
So if I have 6 gallons of water, I’ll need 3 cups of sugar because 3 is ½ of 6

3. Writing Function Rules
Write a function rule for “The output is five less than the input.”
Words The output is five less than the input.
Equation y = x - 5

4. Writing Function Rules
Write a function rule for “The output is the square of the input.”

5. Writing Function Rules
Write a function rule for “The output is the square of the input.”
Words The output is the square of the input.
Equation y = x²
Write a function rule for “The output is one-fourth of the input.”

6. Evaluating a Function What is the value of y when x = 5 ?
What is the value of y = 2x + 5 when x = 3 ?
Step #1: Write the equation y = 2x + 5
Step #2: Plug in 3 for x y = 2(3) + 5
Step #3: Solve the problem y = 6 + 5
y = 11
Answer: When x = 3, y = 11
What is the value of y when x = 5 ?

7. Evaluating a Function
Find the value of y when x = 5 y = 4x – 1 y = 10x y = 7 – 3x

8. Function as a Table The table below represents the function y = x + 2
Input, x
Output, y
Ordered Pair,
(x, y) 1 3
(1, 3) 2 4
(2, 4) 5
(3, 5)

9. Function as a Graph

10. Graph the Function y = -2x + 1
Use the following inputs: -1, 0, 1, and 2
Input, x
-2x + 1
Output, y
Ordered Pair (x, y) -1
-2 (-1) + 1
(-1, )
-2 (0) + 1
(0, ) 1
-2 (1) + 1
(1, ) 2
-2 (2) + 1
(2, )

11. Graph the Function y = -2x + 1
Use the following inputs: -1, 0, 1, and 2
Input, x
-2x + 1
Output, y
Ordered Pair (x, y) -1
-2 (-1) + 1 3
(-1, 3)
-2 (0) + 1 1
(0, 1)
-2 (1) + 1
(1, -1) 2
-2 (2) + 1 -3
(2, -3)

12. Graph the Function y = -2x + 1

13. Graph the Functions
Use your own inputs (suggestion: 1, 2, 3) to graph the following functions:
y = x +1
y = -3x
y = 3x + 2

14. Word Problem
The number of pounds (p) of carbon dioxide produced by a car is 20 times the number of gallons (g) of gasoline used by the car. Write and graph a function that describes the relationship between g and p. Words : The number of pounds is 20 times the number of gallons of carbon dioxide of gasoline used Equation: p = 20  g

15. Input – Output Table Input, g 20 Output, p Ordered Pair (g, p) 1
20 (1)
(1, 20) 2
20 (2) 40
(2, 40) 3
20 (3) 60
(3, 60)
Because you can’t have a negative number of gallons, use only positive values of g

16. Plot the Ordered Pairs and Connect Them

17. Homework
Page 253 (Handout) (#1, 4, 5, 6, 7, 8, 9, 12, 13, 15, 17, 19, 21, 26, 28, 30)