Blitzer - College Algebra 8th Edition

Ch. 3 - Polynomial and Rational Functions

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Blitzer 8th Edition

Ch. 3 - Polynomial and Rational Functions

Section 3.6

Problem 35

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $x^{3} + 2 x^{2} - x - 2 \geq 0$

Problem 36

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $x^{3} + 2 x^{2} - 4 x - 8 \geq 0$

Problem 37

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $x^{3} - 3 x^{2} - 9 x + 27 < 0$

Problem 39

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $x^{3} + x^{2} + 4 x + 4 > 0$

Problem 41

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $x cubed is greater than or equal to 9 x squared$

Problem 42

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x³≤4x²

Problem 43

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x−4)/(x+3) > 0

Problem 45

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x+3)/(x+4)<0

Problem 47

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (−x+2)/(x−4)≥0

Problem 48

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (−x−3)/(x+2)≤0

Problem 49

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (4−2x)/(3x+4)≤0

Problem 50

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (3x+5)/(6−2x)≥0

Problem 51

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. x/(x−3)>0

Problem 52

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x+4)/x>0

Problem 53

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x+4)(x−1)/(x+2)≤0

Problem 55

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x + 1)/(x + 3) < 2

Problem 57

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x + 4)/(2x - 1) ≤ 3

Problem 58

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation.1/(x - 3) < 1

Problem 59

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x - 2)/(x + 2) ≤ 2

Problem 60

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. x/(x + 2) ≥ 2

Problem 61

Find the domain of each function. $f(x) = \sqrt{2x^2 - 5x + 2}$

Problem 62

Find the domain of each function. $f(x) = \frac{1}{\sqrt{4x^2 - 9x + 2}}$

Problem 63

Find the domain of each function. $f(x) = \sqrt{\frac{2x}{x + 1} - 1}$

Problem 64

Find the domain of each function. $f(x) = \sqrt{\frac{x}{2x - 1} - 1}$

Problem 65

Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. |x² + 2x - 36| > 12

Problem 67

Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. 3/(x +3) > 3/(x - 2)

Problem 68

Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. 1/(x + 1) > 2/(x - 1)

Problem 69

Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. $(x^{2} - x - 2) / (x^{2} - 4 x + 3) > 0$

Problem 71

In Exercises 71–72, use the graph of the polynomial function to solve each inequality.

$2 x^{3} + 11 x^{2} \geq 7 x + 6$

Problem 72

In Exercises 71–72, use the graph of the polynomial function to solve each inequality.

2x³ + 11x² < 7x + 6