1. Copyright © Ed2Net Learning, Inc.1 Algebra Grade 5

2. Copyright © Ed2Net Learning, Inc.2 Warm Up Solve each equation. Use models if necessary  6x = 24  7y = -42  -12 = 5m  4p = 11

3. Copyright © Ed2Net Learning, Inc.3 Functions A function rule describes the relationship between the input and the output of a function. The inputs and outputs can be organized in a function table.

4. Copyright © Ed2Net Learning, Inc.4 Functions Example 1  Complete the function table.  The function rule is x – 7. Subtract 7 from each input. Input (x)Output (x -7) 9 8 6 Input Output 9- 72 8- 71 6- 7 -2 Input (x)Output (x -7) 92 81 6

5. Copyright © Ed2Net Learning, Inc.5 Functions Example 2  Find the rule for the function table.  Study the relationship between each input and output.  The output is 4 times the input. So, the function rule is 4x. Input (x)Output ( ) -3-12 14 28 Input Output -3x 4 -12 1x 44 2x 4 8

6. Copyright © Ed2Net Learning, Inc.6 Your Turn! Complete the function table. Input (x)Output (x + 4) -2 1 4

7. Copyright © Ed2Net Learning, Inc.7 Your Turn! Find the rule for the function table. Input (x)Output ( ) -3 11/3 62

8. Copyright © Ed2Net Learning, Inc.8 Solve a problem using a function A criminalist knows that an adult male’s height, in centimeters, is about 72 centimeters more than 2.5 times the length of his tibia, t (shin bone). How tall is a man whose tibia is 30 centimeters?  First, let us determine the function rule.  Let t = length of tibia  The function rule is 2.5t + 72  Then, replace t in the rule 2.5t + 72 with the length of the tibia, 30.  2.5t + 72 = 2.5(30) + 72 = 75 + 72 = 147  The man is about 147 centimeters tall. 72 centimeters more than means to add 72.

9. Copyright © Ed2Net Learning, Inc.9 Your Turn! Nina buys a refillable mug for $4.50 on her first day at a new job. Starting with her second day, she gets a refill of coffee costing $2.00 every day on the way to work. How much does she spend on coffee in her first 8 workdays?

10. Copyright © Ed2Net Learning, Inc.10 Graphing Functions Make a function table for rule y = 3x. Use input values of -2, 0, and 2. Then graph the function. Step 1: Record the input and output in a function table. List the input and output as ordered pairs. InputFunction Rule OutputOrdered Pairs (x)(3x)(y)(x,y) -23(-2)-6(-2,-6) 03(0)0(0,0) 23(2)6(2,6)

11. Copyright © Ed2Net Learning, Inc.11 Graphing Functions Step 2: Graph the ordered pairs on the coordinate plane. 0x y (2,6) (-2,-6) (0,0) The y-coordinates represent the output values. The x-coordinates represent the input values. The set of ordered pairs [(-2,-6), (0,0), (2,6) is called a relation.

12. Copyright © Ed2Net Learning, Inc.12 Graphing Functions Step 3: The points appear to lie on a line. Draw the line that contains these points. The line is the graph of y=3x. 0x y For any point on this line, y = 3x

13. Copyright © Ed2Net Learning, Inc.13 Your Turn! Make a function table for the rule y = x + 2. Use input values of -4, 0, and 4. Then graph the function.

14. Copyright © Ed2Net Learning, Inc.14 Make a Function Table for a Graph Make a function table for the graph. The determine the function role. Use the ordered pair to make a function table. Study the input and output. Look for a rule. 0x y Input (x)Output (y)(x,y) -4(-4,-1) -21(-2,1) 03(0,3) 25(2,5) (-2,1) (-4,-1) (2,5) (0,3) Input Output -4+ 3 -1 -2+ 3 1 0+ 3 3 2 + 3 5 3 is added to each input to get the output. The function role is y = x + 3

15. Copyright © Ed2Net Learning, Inc.15 Your Turn! Make a function table for the graph. The determine the function role. 0x y (0,0) (4,8) (2,4)

16. Copyright © Ed2Net Learning, Inc.16 Nonlinear Function A function whose graph is not a straight line is called a nonlinear function 0x y (0,0) (2,4) (1,1) Input (x)Output (x 2 ) -24 1 00 11 24 (-1,1) (-2,4)

17. Copyright © Ed2Net Learning, Inc.17 Break!

18. Copyright © Ed2Net Learning, Inc.18

19. Copyright © Ed2Net Learning, Inc.19 Assessment 1. Complete the function table. 2. Complete the function table. Input (x)Output (x - 2) -2 1 4 Input (x)Output (2x) 0 3

20. Copyright © Ed2Net Learning, Inc.20 Assessment 3. Find the rule for the function table. 4. Find the rule for the function table. Input (x)Output ( ) -3-12 14 416 Input (x)Output ( ) 4 83 105

21. Copyright © Ed2Net Learning, Inc.21 Assessment 5. Make a function table for the rule y = x - 2. Use input values of 0, 2, and 4. Then graph the function. 6. Make a function table for the rule y = 2x. Use input values of -1, 1, and 2. Then graph the function.

22. Copyright © Ed2Net Learning, Inc.22 Assessment 7. Make a function table for each graph. Then determine the function rule. 8. Make a function table for each graph. Then determine the function rule. 0x y (2,-1) (6,3) (4,1) 0 x y (-2,-1) (4,2) (2,1)

23. Copyright © Ed2Net Learning, Inc.23 Assessment 9. Fresno, California, f, and Buffalo, New York, b, are 3 times zones apart. Use the function rule f = b – 3 to find the time in Buffalo when it is 3:30pm in Fresno. 10. A catalog that sells gift wrap charges $3 for each roll of gift wrap ordered and an additional $1 for shipping of each roll. Write a function rule that can be used to find the cost, including shipping, of any number of rolls of gift wrap.

24. Copyright © Ed2Net Learning, Inc.24 Great Job! Remember to do the practice worksheets!!!