Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4.

$\text{ƒ}\left(x\right)=x^3+x^2-36x-36$

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(4-3x)/(2x+1)

Simple Interest Simple interest varies jointly as principal and time. If $1000 invested for 2 yr earned $70, find the amount of interest earned by $5000 invested for 5 yr.

Solve each polynomial inequality. Give the solution set in interval notation. 2x³ - 7x² ≥ 3 - 8x

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x² - 5x+1; k = 2+i

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=-x³+x²+2x

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -(x - 2)² - 5

Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4.

$\text{ƒ}\left(x\right)=-3x^4-5x^3+2x^2$

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(2x+6)/(x-4)

Solve each polynomial inequality. Give the solution set in interval notation. x⁴ - x³ - 10x² - 8x < 0

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x² + 4; k = 2i

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = x² - 4x + 3

Force of Wind The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. If a wind of 40 mph exerts a force of 50 lb on a surface of 1/2 ft², how much force will a wind of 80 mph place on a surface of 2 ft²?

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(x²-1)/(x+3)

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x³(x²-4)(x-1)

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4.

$\text{ƒ}\left(x\right)=(x^2+4)/(x-1)$

Solve each problem. Give the maximum number of turning points of the graph of each function. ƒ(x)=4x^3-6x^2+2

Solve each polynomial inequality. Give the solution set in interval notation. x⁴ + 2x³ + 36 < 11x² + 12x

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x³-5x²-x+6

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -2x² - 8x - 7

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(x²-2x-3)/(2x²-x-10)

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 2x⁵ - 10x³ - 19x² - 50; k=3

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -3x² + 18x + 1

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x⁴+x³-6x²-7x-2

Period of a Pendulum The period of a pendulum varies directly as the square root of the length of the pendulum and inversely as the square root of the acceleration due to gravity. Find the period when the length is 121 cm and the acceleration due to gravity is 980 cm per second squared, if the period is 6π seconds when the length is 289 cm and the acceleration due to gravity is 980 cm per second squared.

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 6x⁴ + x³ - 8x² + 5x+6; k=1/2

If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a) domain (b) range (c) end behavior (d) number of zeros (e) number of turning points 10x⁷

Solve each polynomial inequality. Give the solution set in interval notation. x⁵ + x² + 2 ≥ x⁴ + x³ + 2x

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=3x⁴-7x³-6x²+12x+8

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(x²+1)/(x²+9)