3.6_bzca5e

3.6_bzca5e - -2-1 1 2 3-2-1 1 2 Example 2-1 0 1 2-8 2 Solve...

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Section 3.6 Polynomials and Rational Inequalities

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Solving Polynomial Inequalities

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Example 2 Solve and graph the solution set on a real number line: x 12 x - ≤ 10 -5 0 5 10 -

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Example 3 2 Solve and graph the solution set on a real number line: x + x 17 15 x - ≥ - 10 -5 0 5 10 -
Solving Rational Inequalities

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A rational inequality is an inequality that can be put into one of the forms f(x)<0, f(x)>0, f(x) 0 or f(x) 0, where f is a rational function. An example of a rational inequality is 3 3 0 2 4 This inequ x x + + ality is in the form f(x)>0, where f is the rational 3 3 function given by f(x)= . 2 4 We can find the x-intercept of f by setting the numerator equal to 0. 3x+3=0 3x=-3 x=-1 We can determine wher x x + + e f is undefined by setting the denominator equal to 0. 2 4 0 2x=-4 x=-2 x + = -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y 2 -1 0 1 - ( 29 ( 29 , 2 1, -∞ - ∪ - ∞ + + -
Example 5 2 Solve and graph the solution set 0 3 1 x x - + -1 0 1

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Unformatted text preview: -2-1 1 2 3-2-1 1 2 Example 2 -1 0 1 2-8 2 Solve and graph the solution set 3. 4 1 x x + <--2-1 1 2 3-2-1 1 2 Applications Example A student is standing on the top of a university building which is 80 feet tall. If he throws a softball up in the air with an initial velocity of 32 feet/sec, during which time period will the ball' 2 s height exceed that of the university building? s(t)=-16t v t s + + (a) (b) (c) (d) 3 Express the solution set of the following inequality in interval notation x 9 x-≥ ( ] [ ] [ ] [ 29 [ ] [ ] [ ] [ ] , 3 0,3 3,0 3, , 3 0,3 3,0 3,-∞ -∪-∪ ∞-∞ -∪-∪ ∞ (a) (b) (c) (d) Express the solution set in interval notation 5 0. 2 1 x x-≤-( 29 [ 29 1 ,5 2 ,5 5, 1 ,5 2 -∞ ∞...
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3.6_bzca5e - -2-1 1 2 3-2-1 1 2 Example 2-1 0 1 2-8 2 Solve...

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