Exam 2: Polynomial, Power, and Rational Functions

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;

Find the domain of $f(x)=\frac{x^{3}+5 x^{2}-2}{x^{2}-2}$

Identify the horizontal and vertical asymptotes for th function $f(x)=\frac{5 x^{2}}{2 x^{2}-11 x+12}$

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

Describe the end behavior of the polynomial function $f(x)=-6 x^{3}+2 x^{2}+3 x-8$ f(x) \rightarrow -------- as x \rightarrow-\infty; f(x) \rightarrow -------- as x \rightarrow\infty;

Use long division to find the remainder when $x^{4}-3 x^{2}+5 x-1$ is divided by $x^{2}-3$

DATE \@ "M/d/yyyy" 12/6/2020 Find all zeros of $f(x)=x^{3}+7 x-22$ and write a linear factorization of $f(x)$ .

Solve the inequality $\frac{(x-4)^{3}}{x(x+3)} \leq 0$

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?

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

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

Jennifer'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) 2.2 1.1 0.7 1.0 1.7 2.5 3.3 4.0 4.4 3.8 2.8

Graph the function $y=-3 x^{4}+2 x^{3}+6 x^{2}-5 x+1$ 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 remainder when $x^{32}-5 x^{15}+12$ is divided by x+1 ?

In the space below, identify all asymptotes and intercepts of the function $g(x)=\frac{x+6}{x^{2}+x-12}$ 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 (5,-3) and (-1,9) , what is the equation for the parabola?

The manager of 100 apartments knows that at $\$ 600$ rent per month, all apartments will be rented. For each \$25 increase, one apartment will not be occupied. Let $x$ represent the number of $\$ 25$ increases to the rent. (a) Write the revenue as a function of $x$ . (b) What rent per unit will yield maximum revenue? (c) What is the maximum revenue? ch02_p13_20 3/31/10 8:49 AM Page 15

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 $g(x)$ .

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

Find a polynomial of degree 2 with real-number coefficients and zero $3-2 i$