#42. a function is a rule that relates two quantities so that each input value corresponds exactly...

TABLES AND FUNCTIONS

#42

A function is a rule that relates two quantities so that each input value corresponds exactly to one output value.

VOCABULARY

Example 1: Writing Equations from Function Tables

16131074y

1043210x

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.

Example 2

1815129y

106543x

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.

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Example 3

17151311y

158765x

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.

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You can write equations for functions that are described in words.

VIP

Example 4: Translating Words into Math

The height of a painting is 7 times its width.

Write an equation for the function. Tell what each variable you use represents.

Example 5

The height of a mirror is 4 times its width.

Write an equation for the function. Tell what each variable you use represents.

Example 6

A large pie costs $2 more than a small pie.

Write an equation for the function. Tell what each variable you use represents.

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.

Example 7: Problem Solving Application

Example 8

The school band tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $60 for 20 tickets, $66 for 22 tickets, and $81 for 27 tickets. Write an equation forthe function.

Example 9: Finding Solutions of Equations with Two Variables

Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x = 1, 2, 3, 4.

Example 10

Use the given x-values to write solutions of the equation y = 5x + 3 as ordered pairs. x = 2, 3, 4.

Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.

FYI

Example 11: Checking Solutions of Equations with Two Variables

Determine whether the ordered pair is a solution to the given equation.

(3, 21); y = 7x

Example 12

Determine whether the ordered pair is a solution to the given equation.

(6, 4); y = 2x - 7

You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs of some functions, they form a straight line. The equations that express these functions are called linear equations.

VOCABULARY

Example 13: Reading Solutions on Graphs

Use the graph of the linear function to find the value of y for the given value of x.

x = 4

x

y

-4 -2 0 2 4

4

-2

-4

2

Example 14For each graph of a linear function, find the values of y for the values of x given below the graph.x = 0

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10

Example 15For each graph of a linear function, find the values of y for the values of x given below the graph.x = 4

y

2

x 1 2 3 4 5 6 7 8 9 10

9

87

65

0

1

3

4

10

Example 16: Graphing Linear Functions

Graph the function described by the equation. y = 3x+ 2

Example 17

Graph the function described by the equation. y = 8 - x