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

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 -9x⁶

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(4x²+25)/(x²+9)

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=x4+3x³-3x²-11x-6

Use synthetic division to determine whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). ƒ(x) = x² +2x -8; k=2

Graph each polynomial function. ƒ(x)=(x-2)²(x+3)

Solve each polynomial inequality. Give the solution set in interval notation. x⁴ + 6x² + 1 ≥ 4x³ + 4x

Several graphs of the quadratic function ƒ(x) = ax² + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) a < 0; b² - 4ac < 0

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. ƒ(x)=3x²-x-4; 1 and 2

For each polynomial function, find all zeros and their multiplicities. $\text{ƒ}\left(x\right)=(x+1{)}^2(x-1{)}^3(x^2-10)$

Graph each polynomial function. ƒ(x)=2x³+x²-x

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. ƒ(x)=-2x³+5x²+5x-7; 0 and 1

Use synthetic division to determine whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). ƒ(x) = x³ - 3x² + 4x -4; k=2

Several graphs of the quadratic function ƒ(x) = ax² + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) A > 0; b² - 4ac > 0

For each polynomial function, find all zeros and their multiplicities. $\text{ƒ}\left(x\right)=3x(x-2)(x+3)(x^2-1)$

Nuclear Bomb Detonation Suppose the effects of detonating a nuclear bomb will be felt over a distance from the point of detonation that is directly proportional to the cube root of the yield of the bomb. Suppose a 100-kiloton bomb has certain effects to a radius of 3 km from the point of detonation. Find, to the nearest tenth, the distance over which the effects would be felt for a 1500-kiloton bomb.

For each polynomial function, find all zeros and their multiplicities. ƒ(x)=5x²(x²-16)(x+5)

Work each problem. Choices A–D below show the four ways in which the graph of a rational function can approach the vertical line x=2 as an asymptote. Identify the graph of each rational function defined in parts (a) – (d). ƒ(x)=1/(x-2)^2

Work each problem. Choices A–D below show the four ways in which the graph of a rational function can approach the vertical line x=2 as an asymptote. Identify the graph of each rational function defined in parts (a) – (d). $\text{ƒ}\left(x\right)=1/(x-2)$

Work each problem. Choices A–D below show the four ways in which the graph of a rational function can approach the vertical line x=2 as an asymptote. Identify the graph of each rational function defined in parts (a) – (d). $\text{ƒ}\left(x\right)=-1/(x-2)$

Work each problem. Choices A–D below show the four ways in which the graph of a rational function can approach the vertical line x=2 as an asymptote. Identify the graph of each rational function defined in parts (a) – (d). $\text{ƒ}\left(x\right)=-1/(x-2{)}^2$

For each polynomial function, find all zeros and their multiplicities. $\text{ƒ}\left(x\right)=(x^2+x-2{)}^5(x-1+\sqrt{3}{)}^2$

Use synthetic division to determine whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). ƒ(x) = 2x³ - 6x² -9x + 4; k=1

Connecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.)

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. ƒ(x)=2x⁴-4x²+4x-8; 1 and 2

Work each problem. Which function has a graph that does not have a vertical asymptote?

A. ƒ(x)=1/(x²+2)

B. ƒ(x)=1/(x²-2)

C. ƒ(x)=3/x²

D. ƒ(x)=(2x+1)/(x-8)

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. ƒ(x)=x⁴-4x³-x+3; 0.5 and 1

Work each problem. Which function has a graph that does not have a horizontal asymptote?

A. ƒ(x)=(2x-7)/(x+3)

B. ƒ(x)=3x/(x²-9)

C. ƒ(x)=(x²-9)/(x+3)

D. ƒ(x)=(x+5)/(x+2)(x-3)

For each polynomial function, find all zeros and their multiplicities. $\text{ƒ}\left(x\right)=(2x^2-7x+3{)}^3(x-2-\sqrt{5})$

Graph each polynomial function. ƒ(x)=-2x⁴+7x³-4x²-4x