Transcript 10-1

10-1 Tables and Functions
Learn to use data in a table to write an
equation for a function and to use the
equation to find a missing value.
10-1 Tables and Functions
Vocabulary
function
input
output
10-1 Tables and Functions
A function is a rule that relates two
quantities so that each input value
corresponds exactly to one output value.
10-1 Tables and Functions
Additional Example 1: Writing Equations from
Function Tables
Write an equation for a function that gives the
values in the table. Use the equation to find
the value of y for the indicated value of x.
x
y
3
13
4
16
5
19
6
22
7
25
10
Compare x and y to find a
y is 3 times x plus 4.
pattern.
Use the pattern to write an
y = 3x + 4
equation.
y = 3(10) + 4
y = 30 + 4 = 34
Substitute 10 for x.
Use your function rule to find
y when x = 10.
10-1 Tables and Functions
Helpful Hint
When all the y-values are greater than the
corresponding x-values, use addition and/or
multiplication in your equation.
10-1 Tables and Functions
Check It Out: Example 1
Write an equation for a function that gives the
values in the table. Use the equation to find
the value of y for the indicated value of x.
x
y
3
10
4
12
y is 2 times x + 4.
y = 2x + 4
y = 2(10) + 4
y = 20 + 4 = 24
5
14
6
16
7
18
10
Compare x and y to find a
pattern.
Use the pattern to write an
equation.
Substitute 10 for x.
Use your function rule to find
y when x = 10.
10-1 Tables and Functions
You can write equations for functions that are
described in words.
10-1 Tables and Functions
Additional Example 2: Translating Words into
Math
Write an equation for the function. Tell what
each variable you use represents.
The height of a painting is 7 times its width.
h = height of painting
Choose variables for the
equation.
w = width of painting
h = 7w
Write an equation.
10-1 Tables and Functions
Check It Out: Example 2
Write an equation for the function. Tell what
each variable you use represents.
The height of a mirror is 4 times its width.
h = height of mirror
Choose variables for the
equation.
w = width of mirror
h = 4w
Write an equation.
10-1 Tables and Functions
Additional Example 3: Problem
Solving Application
The school choir tracked the number of
tickets sold and the total amount of money
received. They sold each ticket for the
same price. They received $80 for 20
tickets, $88 for 22 tickets, and $108 for 27
tickets. Write an equation for the function.
1
Understand the Problem
The answer will be an equation that describes
the relationship between the number of tickets
sold and the money received.
10-1 Tables and Functions
2
Make a Plan
You can make a table to display the data.
3
Solve
Let t be the number of tickets. Let m be the
amount of money received.
t
m
20
80
22
88
27
108
m is equal to 4 times t.
Compare t and m.
m = 4t
Write an equation.
10-1 Tables and Functions
4
Look Back
Substitute the t and m values in the table to
check that they are solutions of the equation
m = 4t.
m = 4t (20, 80) m = 4t (22, 88) m = 4t (27, 108)
?
80 = 4
?
•
80 = 80
20
?
88 = 4
?
•
88 = 88
22
?
108 = 4
?
•
27
108 = 108
10-1 Tables and Functions
Check It Out: Example 3
The school theater tracked the number of
tickets sold and the total amount of money
received. They sold each ticket for the
same price. They received $45 for 15
tickets, $63 for 21 tickets, and $90 for 30
tickets. Write an equation for the function.
1
Understand the Problem
The answer will be an equation that describes
the relationship between the number of tickets
sold and the money received.
10-1 Tables and Functions
2
Make a Plan
You can make a table to display the data.
3
Solve
Let t be the number of tickets. Let m be the
amount of money received.
t
m
15
45
21
63
30
90
m is equal to 3 times t.
Compare t and m.
m = 3t
Write an equation.
10-1 Tables and Functions
4
Look Back
Substitute the t and m values in the table to
check that they are solutions of the equation
m = 3t.
m = 3t (15, 45) m = 3t (21, 63) m = 3t (30, 90)
?
45 = 3
?
•
45 = 45
15
?
63 = 3
?
•
63 = 63
21
?
90 = 3
?
•
90 = 90
30