Chapter 5 REVIEW SHEET

Chapter 5 REVIEW SHEET - Period 3 Chapter 5 Rational...

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Period 3 Chapter 5 – Rational Functions, Equations, and Inequalities 5.0 – Rational Functions o A Rational Number in form: {a/b | a, b I, b ≠0} o A Rational Expression f(x) , where g(x)≠0 g(x) RECALL: Rational Multiplication: P/Q x R/S = PR/QS Restrictions: Q≠0, S≠0 Rational Division: P/Q ÷ K/L = P/Q x L/K = PL/QK Restrictions: Q≠0, K≠0 Example 1: x 2 – 4 ÷ x + 2 f(x) x – 3 12 – 4x g(x) (x – 2)(x + 2) x -4(x – 3) Reduce by factoring f(x) and g(x). Taking the reciprocal means (x – 3) x + 2 you can multiply (x – 2)(x + 2) 1 x -4(x – 3) 1 Can cross out any common factors, must be separated by (x – 3) 1 x + 2 1 multiplication sign -4(x – 2) Restrictions: x ≠ -2, 3 Example 2: n 2 n 2 – 25 n 2 – 9n +20 n 2 Factor. (n – 5)(n + 5) (n – 5)(n – 4) n (n – 4) – [2(n +5)] Multiply the numerator by all the factors. (n – 5) (n + 5) (n – 4) n 2 – 4n – 2n -10 Expand & Simplify. (n – 5) (n + 5) (n – 4) n 2 – 6n – 10 Restrictions: x≠-5, 5, 4 (n – 5) (n + 5) (n – 4) 5.1 – Graphs of Reciprocal Functions Stationary points occur when y = + 1 on original function (points stay the same) Where y is positive on y = f(x), 1/f(x) stays positive Where y is negative on y = f(x), 1/f(x) stays negative Where y = f(x) is large, 1/f(x) is small. Example (-10, -200) (-10, -1/200) Where y = f(x) is small, 1/f(x) is large. Example (-1, 0.2) (-1, 5)
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