Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. ƒ(x)=2x⁴

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, ∞)?

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(x-2) / {(x-1)(x-3)} > 0

Use synthetic division to perform each division. (5x⁴ +5x³ + 2x² - x-3) / x+1

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. x³-5x²+3x+1; x-1

Solve each problem. If m varies jointly as x and y, and m=10 when x=2 and y=14, find m when x=21 and y=8.

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(x-2) / {(x-1)(x-3)} ≤ 0

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1.

$x^3+6x^2-2x-7;x+1$

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

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. (x⁴ + 4x³ + 2x² + 9x+4) / x+4

Consider the graph of each quadratic function.

a) Give the domain and range.

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

Use synthetic division to perform each division. (3x³+6x²-8x+3)/(x+3)

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.

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)=5x³-3x²+2x-6; k=2

Use the graphs of the rational functions in choices A–D to answer each question.

There may be more than one correct choice. If ƒ represents the function, only one choice has a single solution to the equation ƒ(x)=3. Which one is it?

Solve each quadratic inequality. Give the solution set in interval notation. - ( x +√2)(x-3) < 0

Use synthetic division to perform each division. (x⁵ + 3x⁴ + 2x³ + 2x² + 3x+1) / x+2

Consider the graph of each quadratic function.

(a) Give the domain and range.

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

Solve each quadratic inequality. Give the solution set in interval notation. (x-4)(x + √2) < 0

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. 4x²+2x+54; x-4

Use synthetic division to perform each division. (-9x³ + 8x² - 7x+2) / x-2

Solve each quadratic inequality. Give the solution set in interval notation. (x - 4)² ≤ 0

Solve each problem. Let a be directly proportional to m and n², and inversely proportional to y³. If a=9when m=4, n=9, and y=3, find a when m=6, n=2, and y=5.

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

Solve each quadratic inequality. Give the solution set in interval notation. -(x + 1)² ≥ 0

Use synthetic division to find ƒ(2). ƒ(x)=2x³-3x²+7x-12

Use synthetic division to perform each division. $\frac{\frac{1}{3}{x}^3-\frac{2}{9}{x}^2+\frac{2}{27}x-\frac{1}{81}}{x-\frac{1}{3}}$