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UNIT 4: Rational Functions

UNIT 4: Rational Functions. 8-3 Graphing Rational functions. Rational Functions. Define – Rational Function : is a function with two polynomials (one in the numerator and one in the denominator) Define- P oint of Discontinuity : Value that makes the denominator zero. (holes / asymptotes)

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UNIT 4: Rational Functions

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  1. UNIT 4: Rational Functions 8-3 Graphing Rational functions

  2. Rational Functions • Define – Rational Function: is a function with two polynomials (one in the numerator and one in the denominator) • Define- Point of Discontinuity: Value that makes the denominator zero. (holes / asymptotes) • Hole: point of discontinuity that can be removed (cancelled out with the numerator) • Vertical Asymptote: point of discontinuity that can not be removed (doesn’t cancel with numerator) • Horizontal Asymptote: determine by the degree of numerator and denominator. (more on that later)

  3. Graphing Rational Functions • When graphing rational functions you must find points of discontinuity (holes / asymptotes) 1st -Factor numerator and denominator 2nd – Determine points of discontinuity 3rd – Graph by making a table (or using the table on your calc.) V.A. when: x=5 V.A. when x=1 & x=3 Hole when x=4

  4. Practice V.A. x=-4 Hole: x=2 V.A. x=2/3 Hole: x=3 V.A. x=0 V.A. x=-3 V.A. x=4

  5. Horizontal Asymptotes • To find horizontal asymptotes compare the degree of the numerator “M” to the degree of the denominator “N” • If M < N, then y=0 is horizontal asymptote • If M > N, then No horizontal asymptote • If M=N, then divide leading coefficients

  6. NOTE: The degree is the largest exponent. Horizontal Asymptotes • Determine the horizontal asymptotes M=1 N=1 M=1 N=2 M=2 N=1 H.A. H.A. y=0 NO H.A. If…. M < N, then y=0 M > N, then No HA M=N, then divide leading coefficients

  7. Practice V.A. Holes H.A • Pg 521 # 17-22 23-28

  8. Word problem • You earn a 75% on the first test of the quarter how many consecutive 100% test scores do you need to bring your test average up to a 95%? Write a rational function. Find when the rational function will be 95% Answer: You will need to make 100% on the next 4 test to bring your test average up to a 95%

  9. Word problem • A Basketball player have made 5 out of the last 7 free throws. How many more consecutive free throws do they need to make to have an average of 80%? Answer: Write a rational function. Find when the rational function will be 80% You will need to make the next 3 free throws for average to be an 80%

  10. Practice word problems • Pg 521 #39,40

  11. Word problem • The function below gives the concentration of the saline solution after adding x milliliters of 0.5% solution to 100 milliliters of 2% solution. • How many ML of the 0.5% solution must be added to have a combined concentration of 0.9%? Answer: (search table) X=275

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