Quiz 2: Polynomial, Power, and Rational Functions

Identify the horizontal and vertical asymptotes for the function $f(x)=\frac{3 x^{2}}{x^{2}-7 x+12}$

An antique vase is projected to be worth $\$ 1,000$ in 2 years and $\$ 1,300$ after 5 years. If the value of the vase continues to appreciate at this same rate, what will it be worth in 8 years?

Find all zeros of $f(x)=x^{3}-x^{2}+x-21$ and write a linear factorization of f(x) .

$\text { Solve the inequality } \frac{(x-5)^{3}}{x(x+2)} \geq 0$ ch02_p13_20 3/31/10 8:49 AM Page 19

In the space below, identify all asymptotes and intercepts of the function $g(x)=\frac{x-5}{x^{2}+x-6}$ . Then sketch a graph of $g(x)$ .

The line x=3 is the axis of symmetry for the graph of a parabola. If the parabola contains the points (1,0) and (4,-3) , what is the equation for the parabola?

Tell how the graph of $y=-3+\frac{4}{x+2}$ can be obtained from the graph of $y=\frac{1}{x}$ by using transformations.

What is the remainder when $x^{29}-7 x^{14}+8$ is divided by x-1 ?

What is the remainder when $x^{32}-5 x^{15}+12$ is divided by x+1 ?

Which one of the following is a polynomial with real coefficients that has 2 and $2-i$ as zeros?

Which one of the following is a polynomial with real coefficients that has -2 and $2+i$ as zeros?

Graph the function $2 x^{4}-3 x^{3}-4 x^{2}+2 x+2$ . Choose a viewing window that shows three local extremum values and all the $x$ -intercepts. Make a sketch of the grapher window, and show the viewing window dimensions.

What is the minimum value for the function $y=2 x^{2}-32 x+256 ?$

Raymond's distance $D$ from a motion detector is given by the data below. Find a cubic regression equation (with coefficients expressed to the nearest thousandth), and graph it together with a scatter plot of the data. t() 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 D(m) 2.8 3.9 4.3 4.0 3.3 2.5 1.8 1.2 0.9 1.6 2.7

A photograph is 4 in. longer than it is wide. If the frame is 2 in. wide, the combined area of the photograph and the frame is $252 \text { in. }$ Find the dimensions of the photograph without the frame.

Divide $x^{3}+3 x^{2}-8 x+7$ by x-2

The value of an antique chair is projected to appreciate $\$ 60$ each year. If the chair will be worth $\$ 650$ in 2 years, what will it be worth in 10 years?

Describe the end behavior of the polynomial function $f(x)=-2 x^{4}-3 x^{3}+3 x-5$ f(x) \rightarrow -------- as x \rightarrow-\infty; f(x) \rightarrow -------- as x \rightarrow\infty;

Solve the inequality $\frac{x-6}{|2 x-4|} 0 .$

Divide $x^{3}-2 x^{2}+4 x-2 \text { by } x-3$