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- Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. See Example 1. ƒ(x)=2x^4
Problem 9
- Use the graphs of the rational functions in choices A–D to answer each question. There may be more than one correct choice. Which choices have domain (-∞, 3)U(3, ∞)?
Problem 9
- Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. x^3-5x^2+3x+1; x-1
Problem 9
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 10
Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1.
Problem 11
Solve each problem. If y varies inversely as x, and y=10 when x=3, find y when x=20.
- Use synthetic division to perform each division. (x^4 + 4x^3 + 2x^2 + 9x+4) / x+4
Problem 11
Problem 11
Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. (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 11a
Consider the graph of each quadratic function.
a) Give the domain and range.
Problem 12
Use synthetic division to perform each division. (3x3+6x2-8x+3)/(x+3)
Problem 12
Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. (a) -(x + 1)(x + 2) ≥ 0 (b) -(x + 1)(x + 2) > 0 (c) -(x + 1)(x + 2) ≤ 0 (d) -(x + 1)(x + 2) < 0
- Use synthetic division to divide ƒ(x) by x-k for the given value of k. Then express ƒ(x) in the form ƒ(x)=(x-k)q(x)+r. ƒ(x)=5x^3-3x^2+2x-6; k=2
Problem 13
- Use synthetic division to perform each division. (x^5 + 3x^4 + 2x^3 + 2x^2 + 3x+1) / x+2
Problem 13
Problem 13
Solve each problem. Suppose r varies directly as the square of m, and inversely as s. If r=12 when m=6 and s=4, find r when m=6 and s=20.
Problem 13
Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. - ( x +√2)(x-3) < 0
Problem 13a
Consider the graph of each quadratic function.
(a) Give the domain and range.
Problem 14
Use synthetic division to divide ƒ(x) by x-k for the given value of k. Then express ƒ(x) in the form ƒ(x)=(x-k)q(x)+r. ƒ(x)=-3x3+5x-6; k=-1
Problem 14
Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. (x-4)(x + √2) < 0
- Use synthetic division to perform each division. (-9x^3 + 8x^2 - 7x+2) / x-2
Problem 15
Problem 15
Solve each problem. Let a be directly proportional to m and n^2, and inversely proportional to y^3. If a=9when m=4, n=9, and y=3, find a when m=6, n=2, and y=5.
Problem 15
Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. (x - 4)^2 ≤ 0
- Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. 4x^2+2x+54; x-4
Problem 15
- Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x - 4)^2 - 3
Problem 15
Problem 16
Use synthetic division to find ƒ(2). ƒ(x)=2x3-3x2+7x-12
Problem 16
Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. -(x + 1)2 ≥ 0
- Use synthetic division to find ƒ(2). ƒ(x)=5x^4-12x^2+2x-8
Problem 17
Problem 17
Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as x. (y=kx)
Problem 17
Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. x2 + x - 30 ≤ 0
- Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x + 4)^2 - 3
Problem 17
- Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. x^3+2x^2+3; x-1
Problem 17
