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Warm-Up 3/27

Warm-Up 3/27. 1. G. Rigor: You will learn how to analyze, graph and solve equations of rational functions. Relevance: You will be able to use graphs and equations of rational functions to solve real world problems. . 2-5a Rational Functions.

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Warm-Up 3/27

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  1. Warm-Up 3/27 1. G

  2. Rigor:You will learn how to analyze, graph and solve equations of rational functions. Relevance:You will be able to use graphs and equations of rational functions to solve real world problems.

  3. 2-5a Rational Functions

  4. A rational function is the quotient of two polynomial functions. An asymptote is a line or curve that a graph approaches.

  5. If a factor is removable, then there is a hole at that x value.

  6. Example 1a: Find the domain of the function and the equations of the vertical or horizontal asymptotes, if any. Step 1 Find the domain. Step 2 Find the asymptotes, if any. Degree of numerator equals the degree of the denominator, so is the horizontal asymptote. Check

  7. Example 1b: Find the domain of the function and the equations of the vertical or horizontal asymptotes, if any. Step 1 Find the domain. Step 2 Find the asymptotes, if any. Degree of numerator equals the degree of the denominator, so therefore is the horizontal asymptote. Check

  8. Example 2a: Find the domain, the vertical or horizontal asymptotes and intercepts. Then graph the function. Step 1 Find the domain. Step 2 Find the asymptotes, if any. Degree of numerator less than the degree of the denominator, so is the horizontal asymptote. Step 3 There are no x-intercepts and (0, 2) is the y-intercept. Step 4

  9. Example 2b: Find the domain, the vertical or horizontal asymptotes and intercepts. Then graph the function. Step 1 Find the domain. Step 2 Find the asymptotes, if any. Degree of numerator greater than the degree of the denominator, so no horizontal asymptote. Step 3 x-intercepts (5, 0) & (2, 0) and (0,) is the y-intercept. Step 4

  10. Example 3: Find the domain, the vertical or horizontal asymptotes and intercepts. Then graph the function. Step 1 Find the domain. Step 2 Find the asymptotes, if any. Degree of numerator is equal to the degree of the denominator, so 𝑦 = 3is the horizontal asymptote. Step 3 x-intercepts (– 1, 0) & (1, 0) and (0,) is the y-intercept. Step 4

  11. An oblique asymptote is a slant line that occurs when the degree of the numerator is exactly one more than the degree of the denominator.

  12. Example 4: Find the domain, any asymptotes and intercepts. Then graph the function. Step 1 Find the domain. Step 2 Find the asymptotes, if any. Degree of numerator is exactly one more than the degree of the denominator, so No H. A. &𝑦 = 2x – 2 is the oblique asymptote. Step 3 x- & y-intercept (0, 0). Step 4

  13. Example 5: Find the domain, any asymptotes, holes and intercepts. Then graph the function. Step 1 Find the domain. Step 2 Find the asymptotes, if any. Degree of numerator is equal to the degree of the denominator, so 𝑦 = 1 is the horizontal asymptote. Step 3 x-intercept (2, 0) and (0,) is the y-intercept. Step 4

  14. math! • 2-5a Assignment: TX p138, 4-28 EOE

  15. Warm-Up 3/26 1. A

  16. math! • 2-5a Assignment: TX p138, 4-28 EOE

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