Follow the seven steps to graph each rational function. f(x)=x⁴/(x²+2)

When 2x²−7x+9 is divided by a polynomial, the quotient is 2x-3 and the remainder is 3. Find the polynomial.

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(x²+x−12)/(x²−4)

Use synthetic division to show that 5 is a solution of x^4−4x^3−9x^2+16x+20=0. Then solve the polynomial equation.

Solve the variation problems in Exercises 77–82. The distance that a body falls from rest is directly proportional to the square of the time of the fall. If skydivers fall 144 feet in 3 seconds, how far will they fall in 10 seconds?

Solve the variation problems in Exercises 77–82. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet?

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(3x²+x−4)/(2x²−5x)

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x²−1)/x

Find the inverse of f(x)=(x−10)/(x+10).

Exercises 82–84 will help you prepare for the material covered in the next section. Solve: x²+4x−1=0

Exercises 82–84 will help you prepare for the material covered in the next section. Solve: x²+4x+6=0

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x²+1)/x

Exercises 82–84 will help you prepare for the material covered in the next section. Let f(x)=an(x⁴−3x²−4). If f(3)=−150, determine the value of a_n.

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x²+x−6)/(x−3)

Solve each inequality in Exercises 86–91 using a graphing utility. x² + 3x - 10 > 0

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x³+1)/(x²+2x)

Solve each inequality in Exercises 86–91 using a graphing utility. 2x² + 5x - 3 ≤ 0

Solve each inequality in Exercises 86–91 using a graphing utility. x³ + x² - 4x - 4 > 0

In Exercises 89–94, the equation for f is given by the simplified expression that results after performing the indicated operation. Write the equation for f and then graph the function. 5x²/(x²−4) ⋅ (x²+4x+4)/(10x³)

Solve each inequality in Exercises 86–91 using a graphing utility. (x - 4)/(x - 1) ≤ 0

In Exercises 89–94, the equation for f is given by the simplified expression that results after performing the indicated operation. Write the equation for f and then graph the function. x/(2x+6) − 9/(x²−9)

Solve each inequality in Exercises 86–91 using a graphing utility. 1/(x + 1) ≤ 2/(x + 4)

In Exercises 89–94, the equation for f is given by the simplified expression that results after performing the indicated operation. Write the equation for f and then graph the function. (1 − 3/(x+2)) / (1 + 1/(x−2))

Use long division to rewrite the equation for g in the form quotient + remainder/divisor. Then use this form of the function's equation and transformations of f(x) = 1/x to graph g. g(x) = (2x+7)/(x+3)

Use long division to rewrite the equation for g in the form quotient + remainder/divisor. Then use this form of the function's equation and transformations of f(x) = 1/x to graph g. g(x)=(3x−7)/(x−2)

In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-4) The graph passes through the point (1,4).

In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-1) The graph passes through the point (-2,-3).

Find the average rate of change of f(x)=√x from x₁=4 to x₂=9.

Solve: $x^4-6x^3+4x^2+15x+4=0$.