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Mrs. Rivas International Studies Charter School. Rational Functions.

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Presentation on theme: "Mrs. Rivas International Studies Charter School. Rational Functions."— Presentation transcript:

1 Mrs. Rivas International Studies Charter School. Rational Functions

2 Mrs. Rivas International Studies Charter School. Finding the Domain of a Rational Function Example 1 Find the domain of each rational function: a.

3 Mrs. Rivas International Studies Charter School. Finding the Domain of a Rational Function Example 1 Find the domain of each rational function: b.

4 Mrs. Rivas International Studies Charter School. Finding the Domain of a Rational Function Example 1 Find the domain of each rational function: c.

5 Mrs. Rivas International Studies Charter School.

6 Mrs. Rivas International Studies Charter School.

7 Mrs. Rivas International Studies Charter School.

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9 Mrs. Rivas International Studies Charter School.

10 Mrs. Rivas International Studies Charter School.

11 Mrs. Rivas International Studies Charter School.

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15 Mrs. Rivas International Studies Charter School. Identify Vertical Asymptotes of Rational Functions The graph of a rational function never intersects a vertical asymptote. We will use dashed lines to show asymptotes.

16 Mrs. Rivas International Studies Charter School.

17 Mrs. Rivas International Studies Charter School.

18 Mrs. Rivas International Studies Charter School. Finding the Vertical Asymptotes of a Rational Function Example 2 Find the vertical asymptotes, if any, of the graph of each rational function: a.

19 Mrs. Rivas International Studies Charter School. Finding the Vertical Asymptotes of a Rational Function Example 2 Find the vertical asymptotes, if any, of the graph of each rational function: a.

20 Mrs. Rivas International Studies Charter School. Finding the Vertical Asymptotes of a Rational Function Example 2 Find the vertical asymptotes, if any, of the graph of each rational function: b.

21 Mrs. Rivas International Studies Charter School. Finding the Vertical Asymptotes of a Rational Function Example 2 Find the vertical asymptotes, if any, of the graph of each rational function: c.

22 Mrs. Rivas International Studies Charter School. Two Graphs with Vertical Asymptotes, one without

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25 Mrs. Rivas International Studies Charter School. Identify Horizontal Asymptotes

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29 Mrs. Rivas International Studies Charter School. Finding the horizontal Asymptotes of a Rational Function Example 3 Find the horizontal asymptote, if any, of the graph of each rational function: a.

30 Mrs. Rivas International Studies Charter School. Finding the horizontal Asymptotes of a Rational Function Example 3 Find the horizontal asymptote, if any, of the graph of each rational function: b.

31 Mrs. Rivas International Studies Charter School. Finding the horizontal Asymptotes of a Rational Function Example 3 Find the horizontal asymptote, if any, of the graph of each rational function: c. The degree of the numerator, 3, is greater than the degree of the denominator, 2. Thus, the graph of has no horizontal asymptote

32 Mrs. Rivas International Studies Charter School. Use transformations to graph rational functions. Some rational functions can be graphed using transformations (horizontal shifting, stretching or shrinking, reflecting, vertical shifting) of these two common graphs.

33 Mrs. Rivas International Studies Charter School. Using Transformations to Graph a Rational Function Example 4

34 Mrs. Rivas International Studies Charter School. Graphing Rational Functions

35 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 5 Graph: Step 1 Step 1 Determine symmetry.

36 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 5 Graph: Step 3 Step 3 Find the x-intercept(s).

37 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 5 Graph: Step 4 Step 4 Find the vertical asymptote(s).

38 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 5 Graph: Step 5 Step 5 Find the horizontal asymptote.

39 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 5 Graph: Step 6 Step 6 Plot points between and beyond each x-intercept and vertical asymptote.

40 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 6 Graph: Step 1 Step 1 Determine symmetry.

41 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 6 Graph: Step 3 Step 3 Find the x-intercept(s). Step 4 Step 4 Find the vertical asymptote(s).

42 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 6 Graph: Step 4 Step 4 Find the vertical asymptote(s).

43 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 6 Graph: Step 5 Step 5 Find the horizontal asymptote.

44 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 6 Graph: Step 6 Step 6 Plot points between and beyond each x-intercept and vertical asymptote. Step 6 Step 6 Plot points between and beyond each x-intercept and vertical asymptote.

45 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 7 Graph: Step 1 Step 1 Determine symmetry.

46 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 7 Graph: Step 3 Step 3 Find the x-intercept(s). Step 4 Step 4 Find the vertical asymptote(s).

47 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 7 Graph: Step 5 Step 5 Find the horizontal asymptote.

48 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 7 Graph: Step 6 Step 6 Plot points between and beyond each x-intercept and vertical asymptote.

49 Mrs. Rivas International Studies Charter School. Graphing a Rational Function Example 7 Graph: Step 7 Step 7 Graph the function

50 Mrs. Rivas International Studies Charter School. Slant Asymptotes

51 Mrs. Rivas International Studies Charter School. Slant Asymptotes

52 Mrs. Rivas International Studies Charter School. Slant Asymptotes

53 Mrs. Rivas International Studies Charter School. Slant Asymptotes

54 Mrs. Rivas International Studies Charter School. Finding the Slant Asymptote of a Rational Function Example 8

55 Mrs. Rivas International Studies Charter School. Finding the Slant Asymptote of a Rational Function Example 8

56 Mrs. Rivas International Studies Charter School.Applications

57 Mrs. Rivas International Studies Charter School.Applications

58 Mrs. Rivas International Studies Charter School. Average Cost for a Business Example 9

59 Mrs. Rivas International Studies Charter School. Average Cost for a Business Example 9

60 Mrs. Rivas International Studies Charter School. Average Cost for a Business Example 9

61 Mrs. Rivas International Studies Charter School. Average Cost for a Business Example 9

62 Mrs. Rivas International Studies Charter School.

63 Mrs. Rivas International Studies Charter School. Time Involved in Uniform Motion Example 10

64 Mrs. Rivas International Studies Charter School. Time Involved in Uniform Motion Example 10

65 Mrs. Rivas International Studies Charter School. Time Involved in Uniform Motion Example 10

66 Mrs. Rivas International Studies Charter School. Time Involved in Uniform Motion Example 10

67 Mrs. Rivas International Studies Charter School Pages: Pages: # Check Points 1-10 and # 2-78 Even Quote “Learning is an ornament in prosperity, a refuge in adversity, and a provision in old age.”Aristotle


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