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Monday

Monday. Starter SOL One A Day Lesson: Relations PPT and Foldable Activity: Create a poster of relations written in 3 methods HW: Worksheet-Relations. SOL One a Day!. In which quadrant is (-2,- I -5 I ) located? I II III IV. Objectives The student will be able to:.

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Monday

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  1. Monday Starter SOL One A Day Lesson: Relations PPT and Foldable Activity: Create a poster of relations written in 3 methods HW: Worksheet-Relations

  2. SOL One a Day! • In which quadrant is (-2,-I-5I) located? • I • II • III • IV

  3. ObjectivesThe student will be able to: 1. identify the domain and range of a relation. 2. show relations as sets and mappings.

  4. How about some more definitions? The domain, (x), input, independent variable is the set of 1st coordinates of the ordered pairs. The range (y), output, dependent variable is the set of 2nd coordinates of the ordered pairs. A relation (x,y) is a set of ordered pairs.

  5. Given the relation {(3,2), (1,6), (-2,0)}, find the domain and range. Domain = {3, 1, -2} Range = {2, 6, 0}

  6. The relation {(2,1), (-1,3), (0,4)} can be shown by 1) a table. 2) a mapping. 3) a graph. x y 2 -1 0 1 3 4 2 -1 0 1 3 4

  7. Given the following table, show the relation, domain, range, and mapping.x -1 0 4 7y 3 6 -1 3 Relation = {(-1,3), (0,6), (4,-1), (7,3)} Domain = {-1, 0, 4, 7} Range = {3, 6, -1, 3}

  8. Mappingx -1 0 4 7y 3 6 -1 3 You do not need to write 3 twice in the range! -1 0 4 7 3 6 -1

  9. Answer Now What is the domain of the relation{(2,1), (4,2), (3,3), (4,1)} • {2, 3, 4, 4} • {1, 2, 3, 1} • {2, 3, 4} • {1, 2, 3} • {1, 2, 3, 4}

  10. Answer Now What is the range of the relation{(2,1), (4,2), (3,3), (4,1)} • {2, 3, 4, 4} • {1, 2, 3, 1} • {2, 3, 4} • {1, 2, 3} • {1, 2, 3, 4}

  11. Inverse of a Relation: For every ordered pair (x,y) there must be a (y,x).Write the relation and the inverse. Relation = {(-1,-6), (3,-4), (3,2), (4,2)} Inverse = {(-6,-1), (-4,3), (2,3), (2,4)} -1 3 4 -6 -4 2

  12. 4 3 -1 2 -3 Answer Now Write the inverse of the mapping. • {(4,-3),(2,-3),(3,-3),(-1,-3)} • {(-3,4),(-3,3),(-3,-1),(-3,2)} • {-3} • {-1, 2, 3, 4}

  13. Tuesday • Starter • SOL One A Day • Homework Huddle • Lesson: Function Machine • Activity: Finish Relations Poster • HW: Worksheet

  14. SOL: One A Day! Which ordered pair (x, y) is a solution to the following? y= 3x+10 (1,11) (−3,1) (−2,16) (2,13)

  15. Wednesday • Substitute

  16. Thursday • Starter • SOL One A Day • I Have Who Has • Lesson: More Functions • Activity: What’s my Rule Game • HW: Worksheet

  17. Friday • Starter • SOL One A Day • Check Homework • Lesson: Graphing Functions • Activity: Spaghetti Bridges-Domain and Range • HW: Worksheet

  18. SOL One A Day

  19. Linear Functions Chapter 7-3 Standards AF 3.3 & AF 1.1 Objective: to identify and graph linear equations.

  20. Vocabulary linear equation linear function

  21. y 6 4 Miles 2 x 0 0 2 4 Hours A linear equation is an equation whose graph is a line. The solutions of a linear equation are the points that make up its graph. Linear equations and linear graphs can be different representations of linear functions. A linear function is a function whose graph is a nonvertical line.

  22. Only two points are needed to draw the graph of a linear function. However, graphing a third point serves as a check. You can use a function table to find each ordered pair.

  23. Graph the linear function y = 4x - 1. Input Ordered Pair Rule Output x 4x – 1 y (x, y) 0 4(0) – 1 –1 (0, –1) 1 4(1) – 1 (1, 3) 3 –1 –5 4(–1) – 1 (–1, –5)

  24. y 4 2 x 0 –2 2 4 –4 –2 –4 Graph the linear function y = 4x - 1. (1, 3) Place each ordered pair on the coordinate grid and then connect the points with a line. (0, –1) (–1, –5)

  25. Graph the linear function y = 3x + 1.

  26. y x Graph the linear function y = 3x + 1. (1, 4) 4 Place each ordered pair on the coordinate grid and then connect the points with a line. 2 (0, 1) 0 –2 2 4 –4 (–1, –2) –2 –4

  27. Dogs are considered to age 7 years for each human year. If a dog is 3 years old today, how old in human years will it be in 4 more years? Write a linear equation which would show this relationship. Then make a graph to show how the dog will age in human years over the next 4 years. Begin by making a function table. Include a column for the rule.

  28. 4-6 Graphing Linear Functions Course 2 Insert Lesson Title Here Check It Out: Example 2 Continued y 7(x) + 21 x Multiply the input by 7 and then add 21. 7(0) + 21 21 0 2 7(2) + 21 35 49 7(4) + 21 4 Let x represent the input and y represent the output. The function is y = 7x + 21, where x is the number of years and y is the total age of the dog in human years.

  29. y 80 60 40 20 0 2 4 8 10 Graph the ordered pairs (0, 21), (2, 35), and (4, 49) from your table. Connect the points with a line. Human Year x Years

  30. Lesson Quiz Graph the linear functions. 1.y = 3x – 4 2.y = –x + 4 3.y = 2 y = –x +4 y = 2 y = 3x – 4

  31. ObjectivesThe student will be able to: 1. To determine if a relation is a function. 2. To find the value of a function. SOL: A.7aef Designed by Skip Tyler, Varina High School

  32. Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x). f(x) y x

  33. Function Notation Input Name of Function Output

  34. 2 3 5 4 3 0 2 3 f(x) f(x) f(x) f(x) Determine whether each relation is a function. 1. {(2, 3), (3, 0), (5, 2), (4, 3)} YES, every domain is different!

  35. 1 4 5 5 6 6 9 3 1 2 f(x) f(x) f(x) f(x) f(x) Determine whether the relation is a function. NO, 5 is paired with 2 numbers! 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}

  36. Answer Now Is this relation a function?{(1,3), (2,3), (3,3)} • Yes • No

  37. Vertical Line Test (pencil test) If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions? FUNCTION! FUNCTION! NOPE!

  38. Vertical Line Test FUNCTION! NO! NO WAY! FUNCTION!

  39. Answer Now Is this a graph of a function? • Yes • No

  40. Given f(x) = 3x - 2, find: = 7 1) f(3) 2) f(-2) 3(3)-2 3 7 = -8 3(-2)-2 -2 -8

  41. Given h(z) = z2 - 4z + 9, find h(-3) (-3)2-4(-3)+9 -3 30 9 + 12 + 9 h(-3) = 30

  42. Answer Now Given g(x) = x2 – 2, find g(4) • 2 • 6 • 14 • 18

  43. Answer Now Given f(x) = 2x + 1, find-4[f(3) – f(1)] • -40 • -16 • -8 • 4

  44. Monday • Starter • SOL One A Day • Check Homework • Lesson: Is it a Function? • Activity: Function Sort • HW: Worksheet

  45. SOL One A Day

  46. Tuesday • Starter • SOL One A Day • Check Homework • Lesson: Domain and Range • Activity: Spaghetti Bridges • HW: Worksheet

  47. SOL One A Day

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