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Problem 84
Graph each rational function. ƒ(x)=(x2+2x+1)/(x2-x-6)
Problem 85
Graph each rational function. ƒ(x)=(20+6x-2x2)/(8+6x-2x2)
Problem 86
Graph each rational function. ƒ(x)=(18+6x-4x2)/(4+6x+2x2)
Problem 107
Find a rational function ƒ having a graph with the given features.
x-intercepts: (-1, 0) and (3, 0)
y-intercept: (0, -3)
vertical asymptote: x=1
horizontal asymptote: y=1
Problem 108
Find a rational function ƒ having a graph with the given features.
x-intercepts: (1, 0) and (3, 0)
y-intercept: none
vertical asymptotes: x=0 and x=2
horizontal asymptote: y=1
Problem 3
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) = 0
Problem 5
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) > 0
Problem 6
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) ≥ 0
Problem 7
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(x-2) / {(x-1)(x-3)} = 0
Problem 8
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(x-2) / {(x-1)(x-3)} < 0
Problem 9
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(x-2) / {(x-1)(x-3)} > 0
Problem 10
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(x-2) / {(x-1)(x-3)} ≤ 0
Problem 11
Solve each quadratic inequality. Give the solution set in interval notation.
(a) (x - 5)(x + 2) ≥ 0
(b) (x - 5)(x + 2) > 0
(c) (x - 5)(x + 2) ≤ 0
(d) (x - 5)(x + 2) < 0
Problem 12
Solve each quadratic inequality. Give the solution set in interval notation.
(a) -(x + 1)(x + 2) ≥ 0
(b) -(x + 1)(x + 2) > 0
(c) -(x + 1)(x + 2) ≤ 0
(d) -(x + 1)(x + 2) < 0
Problem 13
Solve each quadratic inequality. Give the solution set in interval notation. - ( x +√2)(x-3) < 0
Problem 14
Solve each quadratic inequality. Give the solution set in interval notation. (x-4)(x + √2) < 0
Problem 15
Solve each quadratic inequality. Give the solution set in interval notation. (x - 4)2 ≤ 0
Problem 16
Solve each quadratic inequality. Give the solution set in interval notation. -(x + 1)2 ≥ 0
Problem 17
Solve each quadratic inequality. Give the solution set in interval notation. x2 + x - 30 ≤ 0
Problem 19
Solve each quadratic inequality. Give the solution set in interval notation. x2 - 2 > x
Problem 21
Solve each quadratic inequality. Give the solution set in interval notation. 2x2 + 5 ≤ 11x
Problem 23
Solve each polynomial inequality. Give the solution set in interval notation.
(a) -x(x - 1)(x - 2) ≥ 0
(b) -x(x - 1)(x - 2) > 0
(c) -x(x - 1)(x - 2) ≤ 0
(d) -x(x - 1)(x - 2) < 0
Problem 27
Solve each polynomial inequality. Give the solution set in interval notation. (x - 4)(2x + 3)(3x - 1) ≥ 0
Problem 29
Solve each polynomial inequality. Give the solution set in interval notation. (x - 3)(x - 4)(x - 5)2 ≤ 0
Problem 31
Solve each polynomial inequality. Give the solution set in interval notation. -(x - 3)(x - 4)2 (x - 5) > 0
Problem 33
Solve each polynomial inequality. Give the solution set in interval notation. (x + 3)3(2x - 1)(x + 4) ≥ 0
Problem 39
Solve each polynomial inequality. Give the solution set in interval notation. 2x3 - 7x2 ≥ 3 - 8x
Problem 41
Solve each polynomial inequality. Give the solution set in interval notation. x4 - x3 - 10x2 - 8x < 0
Problem 43
Solve each polynomial inequality. Give the solution set in interval notation. x4 + 2x3 + 36 < 11x2 + 12x
Problem 45
Solve each polynomial inequality. Give the solution set in interval notation. x5 + x2 + 2 ≥ x4 + x3 + 2x
