Exam 2: Polynomial, Power, and Rational Functions

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

Which of the following gives the zeros of the graph and their multiplicity?

Use synthetic division to divide $\frac{3 x^{3}-2 x^{2}+5 x-3}{x+2}$ Summarize your results by writing a fraction equation. $\frac{3 x^{3}-2 x^{2}+5 x-3}{x+2}= \frac{\quad\quad\quad\quad\quad\quad\quad\quad\quad}{\quad}$

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.

Use the Remainder Theorem to find the remainder when $x^{3}-6 x^{2}+5 x-2$ is divided by x-6 .

Find all the zeros of $f(x)=x^{4}-x^{3}-x^{2}-x-2$

The formula $h=-16 t^{2}+v_{0} t+s_{0}$ gives the height of an object tossed upward where $v_{0}$ represents the initial velocity, $\boldsymbol{S}_{0}$ represents the initial height, and t represents time. A golf ball is hit straight up from the ground level with an initial velocity of 72 ft/sec. Find the maximum height that the ball reaches and the number of seconds it takes to reach that height.

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.

Tell how the graph of $y=5+\frac{2}{x-4}$ can be obtained from the graph of $y=\frac{1}{x}$ by using transformations.

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?

Solve the inequality $(x-4) \sqrt{x+2} \geq 0$

A contractor purchases a new bulldozer for $\$ 45,000$ . After 15 years the bulldozer will be outdated and have no value. Write a linear equation giving the value $V$ of the equipment during the 15 years it will be used, where $t$ is the number of years after purchase. ch02_p13_20 3/31/10 8:49 AM Page 14

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.

A swimming pool is 8 ft longer than it is wide. The pool is surrounded by a walkway of width 4 ft . The combined area of the pool and the walkway is $1280 \mathrm{ft}^{2}$ Find the dimensions of the pool without the walkway.

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

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

Find all rational zeros of $f(x)=2 x^{3}-x^{2}-23 x-20$

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