Math 104 – Unit 1 Exam – B, 7 & 1 Fall 2011 Name:

To receive credit you must Show your algebraic work unless specifically stated in the problem. Use Exact Answers.

Neatly organize your responses to all problems in the space provided on this test.

1. [15 points] (a) Plot/Label (-1, 1) & (-3, -1). Find the equation of the circle passing through (-3, -1) with center (-1, 1).

(b) Roughly sketch the graph of the circle. (c) Does the graph represent a function? Why or why not?

2. [15 points] Consider the system of equations: {

(a) Find the and intercepts for each equation, use the intercepts to graph the two lines. (Label intercepts)

(b) Solve the system of equations algebraically (exact answer), and label the intersection point on the graph.

Math 104 – Unit 1 Exam – B, 7 & 1 3. [14 points] Find the equation of the line that passes through the point (-3, 4) and is perpendicular to the line .

4. [12 points] Consider the functions 3)( xxf and 13)( 2 xxg . Find the following:

(a) )1)(( fg

(b) )3)(( gf

(c) ))(( xfg

(d) ( You do not have to show any algebraic work on 4(d) ) Are f and g inverses of each other? Why or why not?

Math 104 – Unit 1 Exam – B, 7 & 1

5. [15 points] Consider the function 1)1()( 2 xxm

(a) Identify the parent function and describe the transformations (indicate order) on the parent function to get m .

(b) Use answer in (a) to sketch the graph of m (label at least 3 points).

(c) Is one-to-one (1-1)? Why or why not? (You may answer this graphically)

(d) Determine the range of m . (Answer this graphically)

6. [15 points] Consider the function ( ) √

(a) Algebraically determine domain of (b) Observe that ( by graphing on your calculator.

(c) Is one-to-one (1-1)? Explain why or why not? (You may answer this graphically)

(d) Algebraically find the inverse of (e) State the domain and range of (You may just state answer)

Math 104 – Unit 1 Exam – B, 7 & 1

7. [14 points] Given the piecewise defined function

,3

,2)(

2

x

xxs

0

0

x

x

(a) Sketch the graph of )(xs , label at least 3 points. (b) Use the graph to determine the domain and range of )(xs .

*** BONUS *** [5 extra credit points each] Answer any of the following:

1. Evaluate the difference quotient ( ) ( )

for the function ( )

2. [Gauss-Jordan Elimination] Consider the system of equations below.

(a) In the blank matrix below (on left), form the augmented matrix that represents the system of equations.

(b) Use your calculator to put the matrix in reduced row echelon form, write the reduced matrix below (on right).

(c) Convert the reduced matrix (b) back to a system of equations. Now determine any solution(s) to the original system.

482

102052

24

61233

zyx

zyx

zyx

zyx

part (a)

part (b)