1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up Solve. 1. x + 4 = 19 2. y – 2.3 = 7.8 3. 4z = 120 x = 15
= 8
x = 15
y = 10.1
z = 30 w 9
w = 72

3. Problem of the Day
Substitute the numbers 1, 2, and 3 for the letters a, b, and c in such a way that the number sentence is correct. 1 aa + ab = ac –
a = 2, b = 3, c =1

4. Sunshine State Standards
Prep for MA.7.A.1.4 Graph proportional relationships…
Review of MA.6.A.3.6

5. Vocabulary
function
input
output

6. Rube Goldberg, a famous cartoonist, invented machines that perform ordinary tasks in extraordinary ways. Each machine operates according to a rule, or a set of steps, to produce a particular output.
In mathematics, a function operates according to a rule to produce exactly one output value for each input value. The input is the value substituted into the function. The output is the value that results from the substitution of a given input into the function.

7. A function can be represented as a rule written in words, such as “double the number and add nine to the result,” or by an equation with two variables. One variable represents the input, and the other represents the output.
Function Rule
y = 2x + 9
Output
variable
Input variable
You can use a table to organize and display the input and output values of a function.

8. Additional Example 1A: Completing a Function Table
Find the output for each input.
y = 8x + 5
Input
Rule
Output x
8x + 5 y
Substitute –4 for x. Then simplify. –4
8(–4) + 5
–27
Substitute –2 for x. Then simplify. –2
8(–2) + 5
–11
Substitute 1 for x. Then simplify. 1
8(1) + 5 13

9. Additional Example 1B: Completing a Function Table
Find the output for each input.
y = 4x2
Input
Rule
Output x
4x2 y
Substitute –5 for x. Then simplify. –5
4(–5)2
100
Substitute 0 for x. Then simplify.
4(0)2
Substitute 5 for x. Then simplify. 5
4(5)2
100

10. Check It Out: Example 1A
Find the output for each input.
y = 5x + 3
Input
Rule
Output x
5x + 3 y
Substitute –6 for x. Then simplify. –6
5(–6) + 3
–27
Substitute –3 for x. Then simplify. –3
5(–3) + 3
–12
Substitute 3 for x. Then simplify. 3
5(3) + 3 18

11. Check It Out: Example 1B
Find the output for each input.
y = 3x2
Input
Rule
Output x
3x2 y
Substitute –2 for x. Then simplify. –2
3(–2)2 12
Substitute 0 for x. Then simplify.
3(0)2
Substitute 5 for x. Then simplify. 5
3(5)2 75

12. You can also use a graph to represent a
function. The corresponding input and
output values together form unique
ordered pairs.
An ordered pair is a pair of numbers that represents a point on a graph.
Remember!

13. When writing an ordered pair, write the input value first and then the output value.
Helpful Hint

14. Additional Example 2A: Graphing Functions Using Ordered Pairs
Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. y
y = 3x – 4 4
Ordered
Pair 2
(2, 2)
Input
Rule
Output x
3x – 4 y
(x, y) x –4 –2 2 4
(1, –1) –2
3(–2) – 4
–10
(–2, –10) –2
(0, –4) –1
3(–1) – 4 –7
(–1, –7) –4
3(0) – 4 –4
(0, –4) –6
(–1, –7) 1
3(1) – 4 –1
(1, –1) –8 2
3(2) – 4 2
(2, 2)
(–2, –10)
–10

15. Additional Example 2B: Graphing Functions Using Ordered Pairs
Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs.
y = x2 + 1
Ordered
Pair
Input
Rule
Output y x
x2 + 1 y
(x, y) 6
(–2, 5)
(2, 5) –2
(–2)2 + 1 5
(–2, 5) 4 –1
(–1)2 + 1 2
(–1, 2)
(–1, 2)
(1, 2) 2
(0)2 + 1 1
(0, 1)
(0,1) 1
(1)2 + 1 2
(1, 2) –4 –2 O 2 4 x 2
(2)2 + 1 5
(2, 5)

16. Check It Out: Example 2A
Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. y
y = 2x – 3 4
Ordered
Pair 2
Input
Rule
Output
(2, 1) x
2x – 3 y
(x, y) x –4 –2 2 4
(1, –1) –2
2(–2) – 3 –7
(–2, –7) –2
(0, –3) –1
2(–1) – 3 –5
(–1, –5) –4
(–1, –5)
2(0) – 3 –3
(0, –3) –6 1
2(1) – 3 –1
(1, –1)
(–2, –7) –8 2
2(2) – 3 1
(2, 1)
–10

17. Check It Out: Example 2B
Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. y
y = 6x2
(–2, 24)
(2, 24)
Ordered
Pair
Input
Rule
Output 20 x
6x2 y
(x, y) 16 –2
6(–2)2 24
(–2, 24) 12 –1
6(–1)2 6
(–1, 6) 8
6(0)2
(0, 0)
(–1, 6)
(1, 6) 1
6(1)2 6
(1, 6) 4
(0,0) 2
6(2)2 24
(2, 24) –8 –4 O 4 8 x

18. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

19. 1. Find the output for each input value.
Lesson Quiz: Part I
1. Find the output for each input value.
Input
Rule
Output x
4x – 1 y –2
4(–2) – 1 –9
4(0) – 1 –1 4
4(4) – 1 15

20. Lesson Quiz: Part II
2. Make a function table with three input values for y = x2 – 1, and graph the resulting ordered pairs. x y –2 2 –4 4
(–2, 3)
(2, 3)
(0, –1)
Possible answer:
Output
Ordered Pair
Rule
Input x
x2 – 1 y
(x, y) –2
–22 – 1 3
(–2, 3)
02 – 1 –1
(0, –1) 2
22 – 1 3
(2, 3)

21. Lesson Quiz for Student Response Systems
1. Identify the output for each input.
A B.

22. Lesson Quiz for Student Response Systems
2. Identify a function table for y = x2 – 3, and graph the resulting ordered pairs.
A B.