5.5 Lesson Solving_Rational_Inequalities

5.5 Lesson Solving_Rational_Inequalities - for the...

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MHF 4U0 Name: 5.5 Solving Rational Inequalities Solving a rational inequality means finding all the possible values of the variable that satisfy the inequality. Example #1: The functions ) 7 ( 2 ) ( + = x x x f and ) 2 ( ) ( - - = x x x g are shown on the graph below. Solve each of the following: (a) f(x) = g(x) (b) f(x) < g(x) We can solve rational inequalities algebraically by rearranging the inequality so that one side is equal to 0. We can then use a factor table (interval chart) to determine the sign in each of the intervals created by the zeroes ( x -intercepts) and the vertical asymptotes. Example #2: Solve the following inequalities algebraically. (a) 0 4 2 1 3 - + x x (b) 2 1 1 1 + - < - x x NOTE: What is an equivalent expression
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Unformatted text preview: for the inequality 2 1 1 1 +-<-x x ? pg. 1/3 MHF 4U0 Name: pg. 2/3 Assigned Work: page 295 #1 – 3, 4b, 5d, 6d (algebraically), 9 MHF 4U0 Name: (c) 1 5 2 1 5 2 1 10 2 + + ≥--+-x x x x x Example #3: The equation 2 3 5 ) ( 2 + + = t t t t f models the bacteria count, in thousands, for a sample of tap water that is left to sit over time, t , in days. The function 9 15 ) ( 2 + = t t t g models the bacteria count, in thousands, for a sample of pond water that is also left to sit over several days. Will the bacteria count for the tap water ever exceed the bacteria count for the pond water? Justify your answer. pg. 3/3...
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