1. Introduction to Functions
12-1
Introduction to Functions
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Introduction to Functions
Course 2
12-1
Introduction to Functions
Warm Up
Solve.
1. x + 4 = 19
2. y – 2.3 = 7.8
3. 4z = 120
= 8
x = 15
y = 10.1
z = 30 w 9
w = 72

3. Introduction to Functions
Course 2
12-1
Introduction to Functions
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. Introduction to Functions
Course 2
12-1
Introduction to Functions
Learn to use function tables to generate and graph ordered pairs.

5. Insert Lesson Title Here
Course 2
12-1
Introduction to Functions
Insert Lesson Title Here
Vocabulary
function

6. Introduction to Functions
Course 2
12-1
Introduction to Functions
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 a single output value for each input value.
A function can be represented as a rule written in words, such as “double the number and add nine to the result.”

7. y = 2x + 9 Introduction to Functions 12-1
Course 2
12-1
Introduction to Functions
A function can also be represented by an equation with two variables. One variable represents the input, and the other represents the output.
Rule
y = 2x + 9
Output
Input
You can use a table to organize the input and output values of a function. Your table may show as many possible input and output values as you choose

8. Additional Example 1A: Completing a Function Table
Course 2
12-1
Introduction to Functions
Additional Example 1A: Completing a Function Table
Find the output for each input.
A. y = 8x + 5
Input
Rule
Output x
8x + 5 y
Substitute –4 for x and simplify. –4
8(–4) + 5
–27
Substitute –2 for x and simplify. –2
8(–2) + 5
–11
Substitute 1 for x and simplify. 1
8(1) + 5 13

9. Additional Example 1B: Completing a Function Table
Course 2
12-1
Introduction to Functions
Additional Example 1B: Completing a Function Table
Find the output for each input.
B. y = 4x2
Input
Rule
Output x
4x2 y
Substitute –3 for x and simplify. –3
4(–3)2 36
Substitute 0 for x and simplify.
4(0)2
Substitute 4 for x and simplify. 4
4(4)2 64

10. Introduction to Functions
Course 2
12-1
Introduction to Functions
Try This: Example 1A
Find the output for each input.
A. y = 5x + 3
Input
Rule
Output x
5x + 3 y
Substitute –6 for x and simplify. –6
5(–6) + 3
–27
Substitute –3 for x and simplify. –3
5(–3) + 3
–12
Substitute 3 for x and simplify. 3
5(3) + 3 18

11. Introduction to Functions
Course 2
12-1
Introduction to Functions
Try This: Example 1B
Find the output for each input.
B. y = 3x2
Input
Rule
Output x
3x2 y
Substitute –2 for x and simplify. –2
3(–2)2 12
Substitute 0 for x and simplify.
3(0)2
Substitute 5 for x and simplify. 5
3(5)2 75

12. Introduction to Functions
Course 2
12-1
Introduction to Functions
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. Introduction to Functions
Course 2
12-1
Introduction to Functions
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
Course 2
12-1
Introduction to Functions
Additional Example 2A: Graphing Functions Using Ordered pairs
Make a function table and graph the resulting ordered pairs. y
A. 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 with Ordered Pairs
Course 2
12-1
Introduction to Functions
Additional Example 2B: Graphing Functions with Ordered Pairs
Make a function table and graph the resulting ordered pairs. y
B. y = 5x2
(–2, 20)
(2, 20) 20
Ordered
Pair
Input
Rule
Output 16 x
5x2 y
(x, y) 12 –2
5(–2)2 20
(–2, 20) 8 –1
5(–1)2 5
(–1, 5)
(–1, 5)
(1, 5)
5(0)2 4
(0, 0)
(0,0) 1
5(1)2 5
(1, 5) –8 –4 O 4 8 x 2
5(2)2 20
(2, 20)

16. Introduction to Functions
Course 2
12-1
Introduction to Functions
Try This: Example 2A
Make a function table and graph the resulting ordered pairs. y
A. 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. Introduction to Functions
Course 2
12-1
Introduction to Functions
Try This: Example 2B
Make a function table and graph the resulting ordered pairs. y
B. 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. Introduction to Functions Insert Lesson Title Here
Course 2
12-1
Introduction to Functions
Insert Lesson Title Here
Lesson Quiz: Part 1
Find the output for each input value.
Input
Rule
Output x
4x – 1 y –2 –9 –1 4 15

19. Introduction to Functions Insert Lesson Title Here
Course 2
12-1
Introduction to Functions
Insert Lesson Title Here
Lesson Quiz: Part 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: x y –2 3 –1 2