Exercises 53–60 show incomplete graphs of given polynomial functions. a) Find all the zeros of each function. b) Without using a graphing utility, draw a complete graph of the function. f(x)=3x⁵+2x⁴−15x³−10x²+12x+8

In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function. h(x) = (x^2 - 3x - 4)/(x^2 - x -6)

In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function. r(x) = (x^2 + 4x + 3)/(x + 2)^2

Find the inverse of f(x) = x³ + 2

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

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

Among all pairs of numbers whose sum is 16, find a pair whose product is as large as possible. What is the maximum product?

Follow the seven steps to graph each rational function. f(x)=2x²/(x²−1)

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

Follow the seven steps to graph each rational function. f(x)=−x/(x+1)

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

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

In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function. g(x) = (4x^2 - 16x + 16)/(2x - 3)

Among all pairs of numbers whose difference is 24, find a pair whose product is as small as possible. What is the minimum product?

Follow the seven steps to graph each rational function. f(x)=− 1/(x²−4)

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

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

Follow the seven steps to graph each rational function. f(x)=2/(x²+x−2)

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

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

In Exercises 69–74, solve each inequality and graph the solution set on a real number line. 2x^2 + 5x - 3 < 0

Follow the seven steps to graph each rational function. f(x)=2x²/(x²+4)

In Exercises 69–74, solve each inequality and graph the solution set on a real number line. 2x^2 + 9x + 4 ≥ 0

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(x+2)/(x²+x−6)

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

$2x^3+11x^2\ge 7x+6$

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

2x³ + 11x² < 7x + 6

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(x−2)/(x²−4)

In Exercises 73–74, use the graph of the rational function to solve each inequality.

1/4(x + 2) ≤ - 3/4(x - 2)

In Exercises 73–74, use the graph of the rational function to solve each inequality.

1/4(x + 2) > - 3/4(x - 2)

In Exercises 69–74, solve each inequality and graph the solution set on a real number line. (x + 3)/(x - 4) ≤ 5