September 27 th

1. Thursday, October 3rd Please Complete Warm Up Warm-Up September 27th Find (g•f) G(x)=3x² and f(x)=2x-5 Find Slope (5, -6) and (2,3)

2. Homework Answers Think, Pair, share

3. Combining Functions

4. Writing Fuctions Let f(x)=4x+3 and g(x)=2x+5 f(x) - g(x) Also written (f  g)(x) f(g(x)) Also written (f g)(x)

5. Real-Life application The volume V of a cube with edge length s is given by the function V(s) = s3. Find V(4). Explain what V(4)represents.

6. Identifying a Linear Function by Its Graph

7. Identifying a Linear Function by it’s Table In a linear function, a _________ change in x corresponds to a ___________ change in y.

8. Do you Remember? What should you NOT find in a linear Equation? 1. 2. 3. 4. 5.

9. Function Graphic Organizer

10. Part I: Intercepts

11. What is an INTERCEPT? When you hear the word intercept what do you think of ?

12. Y intercept I. X and Y intercept Definitions X intercept The x coordinate where the graph intersects the x axis. Y coordinate is ALWAYS 0 Example: (3,0) • The y coordinate where the graph intersects the y axis • X coordinate is always 0 • Example: (0,3)

13. X and Y Intercepts Using Graphs • What is the x- intercept? • What is the y-intercept? • How do you know

14. You Try!

15. Question of the Day 2X-3y=20 • If I know that x is always 0 for the y intercept, how could I find it? • If I know that y is always 0 for the x intercept, how could I find it?

16. 5x – 2y = 10 5x – 2y = 10 5x – 2(0) = 10 5(0) – 2y = 10 5x – 0 = 10 0 – 2y = 10 – 2y = 10 5x = 10 y = –5 x = 2 The y-intercept is –5. The x-intercept is 2. #1 Find the x- and y-intercepts. 5x – 2y = 10 To find the x-intercept, replace y with 0 and solve for x. Why can we replace with 0? To find the y-intercept, replace x with 0 and solve for y. Why can we replace with 0?

17. Finding Intercepts in an equation “Cover up Method”

18. 5x – 2y = 10 5x – 2y = 10 5x – 2(0) = 10 5(0) – 2y = 10 5x – 0 = 10 0 – 2y = 10 – 2y = 10 5x = 10 y = –5 x = 2 The y-intercept is –5. The x-intercept is 2. Finding Intercepts in an equation Find the x- and y-intercepts. 5x – 2y = 10 “Cover up”

19. Y intercept #2 2x – 3y = 12 X intercept Cover up the y and solve 2x-3y=12 2x=12 x=6 (6,0) Cover up the x and solve 2x-3y=12 -3y=12 y=-4 (0,-4)

20. –3x + 5y = 30 –3x + 5y = 30 –3(0) + 5y = 30 –3x + 5(0) = 30 0 + 5y = 30 –3x – 0 = 30 5y = 30 –3x = 30 x = –10 y = 6 The x-intercept is –10. The y-intercept is 6. #3 Find the x- and y-intercepts. –3x + 5y = 30

21. 4x + 2y = 16 4x + 2y = 16 4(0) + 2y = 16 4x + 2(0) = 16 0 + 2y = 16 4x + 0 = 16 2y = 16 4x = 16 x = 4 y = 8 The x-intercept is 4. The y-intercept is 8. #4 Find the x- and y-intercepts. 4x + 2y = 16

22. 3x – 7y = 21 3x – 7y = 21 3x – 7(0) = 21 3(0) – 7y = 21 x = 7 Graphing Linear Equations by Using Intercepts Use intercepts to graph the line described by the equation. 3x – 7y = 21 Step 1 Find the intercepts. y-intercept: x-intercept: 3x = 21 –7y = 21 y = –3

23. Step 2: Place intercepts on a graph and connect

24. x Final Product

25. Part 2: Slope and Rate of Change

26. Slope When you think of the word SLOPE…what do you think of?!

27. Slopes are commonly associated with mountains

28. The slope we are studying is associated with the graph of a line

29. Different Slopes zero Positive Undefined Negative

30. POSITIVE SLOPE“Reaching the Goal”

31. Negative Slope“The Tumbler”

32. Zero Slope“Not Much Happening” Horizontal Line

33. Undefined Slope“Only Spider Man”

34. Slope Horizontal vs. Vertical Horizontal: 0Verical: Undefined

35. EquationsHorizontal vs. Vertical Horizontal: y=no xVerical: x=no y

36. How do we find slope Using Graphs?!?!

37. I. Rise and Run Rise= y axis Run= x axis

38. What goes first? You need to rise up before you run

39. Run –9 • Rise 3 Rise –3 • Run 9 Finding Slope with a Graph Find the slope of the line • Begin at one point and count vertically to fine the rise. • Up=Positive • Down=Negative (–6, 5) • Then count horizontally to the second point to find the run. • Right=Positive • Left= Negative (3, 2) It does not matter which point you start with. The slope is the same.

40. Run –5 Rise –2 Rise 2 Run 5 YOU TRY Find the slope of the line Begin at one point and count vertically to find rise. Remember: up=____ down=___ Then count horizontally to the second point to find the run Remember: right=____left=_____ • •

41. Slope in a Table

42. Rate of Change • When you hear the phrase: Rate of Change What do you think of?!??!

43. A rate of change is change in x over the change in Y OR

44. The table shows the average Winter temperature (°F) for five months in Suwanee. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate? Y X dependent: temperatureindependent: month

45. Remember!!!!! ALWAYS

46. 2 to 3 3 to 5 5 to 7 7 to 8 Find the rates of change for all 4 Intervals When was the greatest rate of change?!?!

47. The Slope Formula 1st Ordered Pair (x1, y1) and 2nd Ordered Pair (x2, y2) The letter ‘m’ is used to identify slope.

48. Example #1: (3,4) (5,6)

49. #2 Find the slope of the line that contains (2, 5) and (8, 1) Use the slope formula. Substitute (2, 5) for (x1, y1) and (8, 1) for (x2, y2). Simplify.

50. #3 Find the slope of the line that contains (5, –7) and (6, –4) Use the slope formula. Substitute (5, –7) for (x1, y1) and (6, –4) for (x2, y2). Simplify. = 3 m=3