12-1 Introduction to Functions
Warm Up
Problem of the Day
Lesson Presentation
Course 2
12-1 Introduction to Functions
Warm Up
Solve.
1. x + 4 = 19
2. y – 2.3 = 7.8
x = 15
y = 10.1
3. 4z = 120
z = 30
4. w = 8
w = 72
9
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 + 1
1
1
= c – b
b
a
a
a
a
a
a = 2, b = 3, c =1
Course 2
12-1 Introduction to Functions
Learn to use function tables to generate
and graph ordered pairs.
Course 2
12-1 Introduction
Insert Lesson
Here
toTitle
Functions
Vocabulary
function
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.”
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
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
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
–4
8(–4) + 5
–27
–2
8(–2) + 5
–11
1
8(1) + 5
13
Course 2
Substitute –4 for x
and simplify.
Substitute –2 for x
and simplify.
Substitute 1 for x
and simplify.
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
–3
4(–3)2
36
0
4(0)2
0
4
4(4)2
64
Course 2
Substitute –3 for x
and simplify.
Substitute 0 for x
and simplify.
Substitute 4 for x
and simplify.
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
–6
5(–6) + 3
–27
–3
5(–3) + 3
–12
3
5(3) + 3
18
Course 2
Substitute –6 for x
and simplify.
Substitute –3 for x
and simplify.
Substitute 3 for x
and simplify.
12-1 Introduction to Functions
Try This: Example 1B
Find the output for each input.
B. y = 3x2
Input
Rule
Output
x
3x2
y
–2
3(–2)2
12
0
3(0)2
0
5
3(5)2
75
Course 2
Substitute –2 for x
and simplify.
Substitute 0 for x
and simplify.
Substitute 5 for x
and simplify.
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.
Remember!
An ordered pair is a pair of numbers that
represents a point on a graph.
Course 2
12-1 Introduction to Functions
Helpful Hint
When writing an ordered pair, write the input
value first and then the output value.
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.
A. y = 3x – 4
Input
x
Rule
3x – 4
4
Output
Ordered
Pair
y
(x, y)
–2
3(–2) – 4
–10
(–2, –10)
–1
3(–1) – 4
–7
(–1, –7)
0
3(0) – 4
–4
(0, –4)
1
3(1) – 4
–1
(1, –1)
2
3(2) – 4
2
(2, 2)
Course 2
2
–4 –2
–2
(0, –4)
–4
–6
(–1, –7)
–8
(–2, –10)
–10
y
(2, 2)
2 4
(1, –1)
x
12-1 Introduction to Functions
Additional Example 2B: Graphing Functions with
Ordered Pairs
Make a function table and graph the resulting ordered pairs.
B. y =
Input
x
y
5x2
Rule
Output
Ordered
Pair
5x2
y
(x, y)
–2
5(–2)2
–1
5(–1)2
5
(–1, 5)
0
5(0)2
0
(0, 0)
1
5(1)2
5
(1, 5)
2
5(2)2
20
(2, 20)
Course 2
20
(–2, 20)
20
(2, 20)
16
12
(–2, 20)
8
(–1, 5)
4
(1, 5)
(0,0)
–8
–4 O
4
8
x
12-1 Introduction to Functions
Try This: Example 2A
Make a function table and graph the resulting ordered pairs.
A. y = 2x – 3
4
Output
Ordered
Pair
2x – 3
y
(x, y)
–2
2(–2) – 3
–7
(–2, –7)
–1
2(–1) – 3
–5
(–1, –5)
0
2(0) – 3
–3
(0, –3)
1
2(1) – 3
–1
(1, –1)
2
2(2) – 3
1
(2, 1)
Input
x
Course 2
Rule
2
–4 –2
–2
y
(2, 1)
x
2 4
(1, –1)
(0, –3)
–4
(–1, –5)
–6
(–2, –7) –8
–10
12-1 Introduction to Functions
Try This: Example 2B
Make a function table and graph the resulting ordered pairs.
B. y =
y
6x2
(–2, 24)
Rule
Output
Ordered
Pair
x
6x2
y
(x, y)
–2
6(–2)2
–1
6(–1)2
6
(–1, 6)
0
6(0)2
0
(0, 0)
1
6(1)2
6
(1, 6)
2
6(2)2
Input
Course 2
24
24
(2, 24)
20
16
(–2, 24)
(2, 24)
12
8
(–1, 6)
4
–8
(1, 6)
(0,0)
–4 O
4
8
x
12-1 Introduction
Insert Lesson
toTitle
Functions
Here
Lesson Quiz: Part 1
Find the output for each input value.
Course 2
Input
Rule
Output
x
4x – 1
y
–2
–9
0
–1
4
15
12-1 Introduction
Insert Lesson
toTitle
Functions
Here
Lesson Quiz: Part 2
Make a function table with three input
values for y = x2 – 1, and graph the resulting
ordered pairs.
y
Possible answer:
x
–2
0
2
Course 2
y
3
–1
3
(–2, 3)
4
(2, 3)
2
x
–4
–2
–2
–4
2 4
(0, –1)