Name:    Chapter 4 Pre Test

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

1.

Find the domain of the function and identify any vertical and horizontal asymptotes.

 a. Domain: all real numbers Vertical asymptote: No vertical asymptoteHorizontal asymptote: b. Domain: all real numbers except Vertical asymptote: Horizontal asymptote: c. Domain: all real numbers Vertical asymptote: Horizontal asymptote: d. Domain: all real numbers except Vertical asymptote: No vertical asymptoteHorizontal asymptote: No horizontal asymptote e. Domain: all real numbers except Vertical asymptote: Horizontal asymptote:

2.

Determine the value that the function f approaches as the magnitude of x increases.

 a. b. c. d. e.

3.

Use the below graph to determine any x-intercepts of the graph of the rational function. Set and solve the resulting equation to confirm x-intercepts of the graph of the rational function.

 a. , b. , c. , d. , e. ,

4.

Use the graph of to select the graph of .

 a. d. b. e. c.

5.

The graph of the function

is shown below. Determine the vertical and horizontal asymptotes of its graph.
 a. horizontal: b. horizontal: c. horizontal: d. horizontal: e. horizontal:

6.

Determine 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

7.

Find the vertex and focus of the parabola for the given equation and select its graph.

 a. Vertex: Focus: (,0) d. Vertex: Focus: (,0) b. Vertex: Focus: (,0) e. Vertex: Focus: (0,) c. Vertex: Focus: (,0)

8.

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin.

Focus:
 a. b. c. d. e.

9.

Select the standard form of the equation of the parabola and determine the coordinates of the focus.

 a. ; Focus: b. ; Focus: c. ; Focus: d. ; Focus: e. ; Focus:

10.

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Vertices: ; foci:
 a. b. c. d. e.

11.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin.

Vertices: ; foci:
 a. b. c. d. e.

12.

Identify the conic.

 a. Circle b. Ellipse c. Parabola d. Hyperbola e. Line

13.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin.

vertices: ; foci:
 a. b. c. d. e.

14.

Match the equation with its graph.
 a. b. c. d. e.

15.

Find the vertices and asymptotes of the hyperbola.
 a. vertices:           asymptote: b. vertices:           asymptote: c. vertices:           asymptote: d. vertices:           asymptote: e. vertices:           asymptote:

16.

Find the standard form of the equation of the hyperbola with the given characteristics.
foci:           asymptotes:
 a. b. c. d. e.

17.

Sketch the graph of the ellipse, using the lateral recta.

 a. d. b. e. c.

18.

Describe the translation of the graph of the given conic from the standard position.

 a. Center:, horizontal shift four units to the upward  and vertical shift one unit left b. Center:, horizontal shift four units to the right and vertical shift one unit upward c. Center:, horizontal shift four units to the left and vertical shift one unit downward d. Center:, horizontal shift four units to the right and vertical shift one unit upward e. Center:, horizontal shift four units to the left and vertical shift one unit upward

19.

Describe the translation of the graph of the given conic from the standard position.

 a. Vertex: , horizontal shift five units to the left and vertical shift one unit upward b. Vertex: , horizontal shift five units to the left and vertical shift one unit upward c. Vertex: , horizontal shift five units to the right and vertical shift one unit upward d. Vertex: , horizontal shift five units to the left and vertical shift one unit downward e. Vertex: , horizontal shift five units to the left and vertical shift one unit upward

20.

Find the standard form of the equation of the ellipse with the given characteristics.
center:                     foci:
 a. b. c. d. e.