2 1 Bzca5e
- 1. Section 2.1 Functions and Graphs
- 2. Relations
- 4. Example Find the domain and the range.
- 5. Functions
- 6. A relation in which each member of the domain corresponds to exactly one member of the range is a function. Notice that more than one element in the domain can correspond to the same element in the range. Aerobics and tennis both burn 505 calories per hour.
- 7. Is this a function? Does each member of the domain correspond to precisely one member of the range? This relation is not a function because there is a member of the domain that corresponds to two members of the range. 505 corresponds to aerobics and tennis.
- 9. Example Determine whether each relation is a function?
- 13. Example Determine whether each equation defines y as a function of x.
- 17. Graphing Calculator- evaluating a function
- 18. Example Evaluate each of the following.
- 19. Example Evaluate each of the following.
- 20. Example Evaluate each of the following.
- 22. See the next slide. (2,-1) g(2)=-1 (2,-4) f(2)=-4 2 (1,1) g(1)=1 (1,-2) f(1)=-2 1 (0,3) g(0)=3 (0,0) f(0)=0 0 (-1,5) g(-1)=5 (-1,2) f(-1)=2 -1 (-2,7) g(-2)=7 (-2,4) f(-2)=4 -2 (x,y) g(x)=-2x+3 (x,y) f(x)=-2x x
- 23. f(x) g(x)
- 24. Example Graph the following functions f(x)=3x-1 and g(x)=3x
- 25. The Vertical Line Test
- 26. The first graph is a function, the second is not.
- 27. Example Use the vertical line test to identify graphs in which y is a function of x.
- 28. Example Use the vertical line test to identify graphs in which y is a function of x.
- 29. Obtaining Information from Graphs
- 31. Example Analyze the graph.
- 32. Identifying Domain and Range from a Function’s Graph
- 34. Example Identify the Domain and Range from the graph.
- 35. Example Identify the Domain and Range from the graph.
- 36. Example Identify the Domain and Range from the graph.
- 37. Identifying Intercepts from a Function’s Graph
- 39. Example Find the x intercept(s). Find f(-4)
- 40. Example Find the y intercept. Find f(2)
- 41. Example Find the x and y intercepts. Find f(5).
- 42. (a) (b) (c) (d) Find f(7).
- 43. (a) (b) (c) (d) Find the Domain and Range.
- 44. (a) (b) (c) (d)