#42. A function is a rule that relates two quantities so that each input value corresponds exactly...
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Transcript of #42. A function is a rule that relates two quantities so that each input value corresponds exactly...
![Page 1: #42. A function is a rule that relates two quantities so that each input value corresponds exactly to one output value. VOCABULARY.](https://reader030.fdocuments.in/reader030/viewer/2022032706/56649dde5503460f94ad6a95/html5/thumbnails/1.jpg)
TABLES AND FUNCTIONS
#42
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A function is a rule that relates two quantities so that each input value corresponds exactly to one output value.
VOCABULARY
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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.
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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.
?
![Page 6: #42. A function is a rule that relates two quantities so that each input value corresponds exactly to one output value. VOCABULARY.](https://reader030.fdocuments.in/reader030/viewer/2022032706/56649dde5503460f94ad6a95/html5/thumbnails/6.jpg)
You can write equations for functions that are described in words.
VIP
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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.
![Page 8: #42. A function is a rule that relates two quantities so that each input value corresponds exactly to one output value. VOCABULARY.](https://reader030.fdocuments.in/reader030/viewer/2022032706/56649dde5503460f94ad6a95/html5/thumbnails/8.jpg)
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.
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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.
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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
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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.
![Page 12: #42. A function is a rule that relates two quantities so that each input value corresponds exactly to one output value. VOCABULARY.](https://reader030.fdocuments.in/reader030/viewer/2022032706/56649dde5503460f94ad6a95/html5/thumbnails/12.jpg)
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.
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Example 10
Use the given x-values to write solutions of the equation y = 5x + 3 as ordered pairs. x = 2, 3, 4.
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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
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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
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Example 12
Determine whether the ordered pair is a solution to the given equation.
(6, 4); y = 2x - 7
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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
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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
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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
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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
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Example 16: Graphing Linear Functions
Graph the function described by the equation. y = 3x+ 2
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Example 17
Graph the function described by the equation. y = 8 - x