Check 12-1 HW

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12-2 Graphing Functions

6th Grade Math HOMEWORK

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12-1 Tables and Functions

Our Learning GoalStudents will

understand functions by creating tables and graphing translations.

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12-1 Tables and Functions

Students will understand functions by creating tables and graphing translations.

• Learn to use data in a table to write an equation for a function and to use the equation to find a missing value.

• Learn to represent linear functions using ordered pairs and graphs.

• Learn to use translations to change the positions of figures on a coordinate plane.

• Learn to use reflections to change the positions of figures on a coordinate plane.

• Learn to use rotations to change positions of figures on a coordinate plane.

• Learn to visualize and show the results of stretching or shrinking a figure.

Today’s Learning Goal Assignment

Learn to represent linear functions using ordered pairs and graphs.

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12-2 Graphing Functions

12-2 Graphing Functions

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpWrite an equation for each function. Tell what each variable you use represents.

1. The length of a wall is 4 ft more than three times the height.

2. The number of trading cards is 3 less than the number of buttons.

l = 3h + 4, where l is length and h is height.

c = b – 3, where c is the number of cards and b is the number of buttons.

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12-2 Graphing Functions

Problem of the Day

Steve saved $1.50 each week. How many weeks did it take him to save enough to buy a $45 skateboard?

30

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12-2 Graphing Functions

Vocabulary

linear equation

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12-2 Graphing Functions

Additional Example 1: 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.Make a function table by using the given values for x to find values for y.

x 4x + 2 y

1 4(1) + 2 6

2 4(2) + 2 10

3 4(3) + 2 14

4 4(4) + 2 18

Write these solutions as ordered pairs.

(x, y)

(1, 6)

(2, 10)

(3, 14)

(4, 18)

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12-2 Graphing Functions

Try This: Example 1

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

Make a function table by using the given values for x to find values for y.

x 3x + 2 y

2 3(2) + 2 8

3 3(3) + 2 11

4 3(4) + 2 14

5 3(5) + 2 17

Write these solutions as ordered pairs.

(x, y)

(2, 8)

(3, 11)

(4, 14)

(5, 17)

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12-2 Graphing Functions

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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.

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12-2 Graphing Functions

Additional Example 2: Checking Solutions of Equations with Two Variables

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

(3, 21); y = 7x

y = 7x Write the equation.

21 = 7(3)?

21 = 21?

Substitute 3 for x and 21 for y.

So (3, 21) is a solution to y = 7x.

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12-2 Graphing Functions

Try This: Example 2

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

(4, 20); y = 5x

y = 5x Write the equation.

20 = 5(4)?

20 = 20?

Substitute 4 for x and 20 for y.

So (4, 20) is a solution to y = 5x.

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12-2 Graphing Functions

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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.

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12-2 Graphing Functions

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Additional Example 3: 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

When x = 4, y = 2.

Start at the origin and move 4 units right.

Move up until you reach the graph. Move left to find the y-value on the y-axis.

The ordered pair is (4, 2).

x

y

-4 -2 0 2 4

4

-2

-4

2

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12-2 Graphing Functions

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Try This: Example 3

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

x = 2

When x = 2, y = 4.

Start at the origin and move 2 units right.

Move up until you reach the graph. Move left to find the y-value on the y-axis.

The ordered pair is (2, 4).

x

y

-4 -2 0 2 4

4

-2

-4

2

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12-2 Graphing Functions

Additional Example 4: Graphing Linear Functions

Graph the function described by the equation. y = –x – 2

Make a function table.

x –x – 2 y

–1 –(–1) – 2 –1

0 –(0) – 2 –2

1 –(1) – 2 –3

Write these solutions as ordered pairs.

(x, y)

(–1, –1)

(0, –2)

(1, –3)

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12-2 Graphing Functions

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Additional Example 4 Continued

x

y

Graph the ordered pairs on a coordinate plane.

-5 -4 -3 -2 -1 0 1 2 3 4 5

543

2

1

-5

-4-3-2

-1

Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.

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12-2 Graphing Functions

Try This: Example 4

Graph the function described by the equation. y = –x – 4

Make a function table.

x –x – 4 y

–1 –(– 1) – 4 –3

0 –(0) – 4 –4

1 –(1) – 4 –5

Write these solutions as ordered pairs.

(x, y)

(–1, –3)

(0, –4)

(1, –5)

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12-2 Graphing Functions

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Try This: Example 4

x

y

Graph the ordered pairs on a coordinate plane.

-5 -4 -3 -2 -1 0 1 2 3 4 5

543

2

1

-5

-4-3-2

-1

Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.

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Lesson Quiz

1. Use the given x-values to write solutions as ordered pairs to the equation y = –3x + 1 for x = 0, 1, 2, and 3.

2. Determine whether (4, –2) is a solution to the

equation y = –5x + 3.

3. Graph the function described by the equation

y = –x + 3.

No, –2 ≠ –5(4) + 3

(0, 1), (1, –2), (2, –5), (3, –8)

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12-2 Graphing Functions