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Check 12-1 HW
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Course 1 12-2 Graphing Functions 6 th Grade Math HOMEWORK Page 608 #7-20
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Course 1 12-1 Tables and Functions Our Learning Goal Students will understand functions by creating tables and graphing translations.
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Course 1 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.
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Today’s Learning Goal Assignment Learn to represent linear functions using ordered pairs and graphs. Course 1 12-2 Graphing Functions
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12-2 Graphing Functions Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day
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Warm Up Write 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. Course 1 12-2 Graphing Functions
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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 Course 1 12-2 Graphing Functions
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Vocabulary linear equation Insert Lesson Title Here Course 1 12-2 Graphing Functions
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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. x4x + 2y 14(1) + 26 24(2) + 210 34(3) + 214 44(4) + 218 Write these solutions as ordered pairs. (x, y) (1, 6) (2, 10) (3, 14) (4, 18) Course 1 12-2 Graphing Functions
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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. x3x + 2y 23(2) + 28 33(3) + 211 43(4) + 214 53(5) + 217 Write these solutions as ordered pairs. (x, y) (2, 8) (3, 11) (4, 14) (5, 17) Course 1 12-2 Graphing Functions
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Insert Lesson Title Here 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. Course 1 12-2 Graphing Functions
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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. Course 1 12-2 Graphing Functions
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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. Course 1 12-2 Graphing Functions
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Insert Lesson Title Here 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. Course 1 12-2 Graphing Functions
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Insert Lesson Title Here 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 Course 1 12-2 Graphing Functions
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Insert Lesson Title Here 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 Course 1 12-2 Graphing Functions
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Additional Example 4: Graphing Linear Functions Graph the function described by the equation. y = –x – 2 Make a function table. x–x – 2y –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) Course 1 12-2 Graphing Functions
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Insert Lesson Title Here 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 5 4 3 2 1 -5 -4 -3 -2 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y. Course 1 12-2 Graphing Functions
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Try This: Example 4 Graph the function described by the equation. y = –x – 4 Make a function table. x–x – 4y –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) Course 1 12-2 Graphing Functions
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Insert Lesson Title Here 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 5 4 3 2 1 -5 -4 -3 -2 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y. Course 1 12-2 Graphing Functions
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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) Insert Lesson Title Here Course 1 12-2 Graphing Functions
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