Name:    Chapter 2 Pre Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Determine the vertex of the graph of the quadratic function .
 a. b. c. d. e.

2.

Write the quadratic function in standard form.
 a. b. c. d. e.

3.

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is , express the area, A, as a function of the width, x, of the window.
 a. b. c. d. e.

4.

Find all real zeros of the polynomial and determine the multiplicity of each.
 a. b. c. d. e.

5.

An open box is to be made from a square piece of cardboard, 21 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box.

 a. b. c. d. e.

6.

Use long division to divide.
 a. b. c. d. e.

7.

Use long division to divide.
 a. b. c. d. e.

8.

If , use synthetic division to evaluate .
 a. b. c. d. e.

9.

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
 a. ; b. ; c. ; d. ; e. ;

10.

Simplify the rational expression, , by using long division or synthetic division.
 a. b. c. d. e.

11.

Solve the equation and write complex solutions in standard form.
 a. b. c. d. e.

12.

Find all zeros of the function .
 a. b. c. d. e.

13.

Find a polynomial with real coefficients that has zeros –10, 2i, and –2i.
 a. b. c. d. e.

14.

Find a polynomial with real coefficients that has zeros 3, 3, , and .
 a. b. c. d. e.

15.

Given that is a zero of , find all the zeros of f.
 a. b. c. d. e.

16.

Determine the equations of the vertical and horizontal asymptotes of the graph of the function .
 a. horizontal: ; vertical: b. horizontal: ; vertical: c. horizontal: ; vertical: d. horizontal: ; vertical: e. horizontal: ; vertical:

17.

Determine the zeros (if any) of the rational function .
 a. no zeros b. c. d. e.

18.

Determine the zeros (if any) of the rational function .
 a. b. c. no zeros d. e.

19.

Find the domain of .
 a. all real numbers except b. all real numbers c. all real numbers except d. all real numbers except e. all real numbers except

20.

Find the domain of the function.
 a. b. all real numbers c. d. e.