Name __________________________________
MAT 124 – Fundamentals of Precalculus I
Professor Pestieau
Multiple-Choice Questions
March 5, 2014
Exam 1
[5 pts each]
Circle the correct answer for the following questions.
For questions 1 – 4 below, consider the points A  (3, 2) , B  (6,1) and C  (1, 4) in the
xy -plane. Let l be the line passing through points A and C .

1.
2.
3.
What is the distance between points A and B ?
a.
10
b.
32
c.
82
d.
90
What is the equation, in standard form, of the line parallel to l that passes through B ?
a.
3 x  2 y  20
b.
3x  2 y  20
c.
3 x  2 y  10
d.
3x  2 y  10
What is the equation, in standard form, of the line perpendicular to l that passes
through B ?
a.
2x  3y  9
b.
2 x  3 y  9
c.
2 x  3 y  9
d.
2 x  3 y  9
4.
5.
What is the equation, in general form, of the circle centered at A that passes through
B?
a.
x 2  y 2  6 x  4 y  69  0
b.
x 2  y 2  6 x  4 y  69  0
c.
x 2  y 2  6 x  4 y  94  0
d.
x 2  y 2  6 x  4 y  94  0
What can you say about the graph of y 4  3 y 2 
a.
b.
c.
d.
6.
7.
6
?
x
It is symmetric with respect to the y-axis.
It is symmetric with respect to the x-axis.
It is symmetric with respect to the origin.
It has no symmetries.
What is the domain of the function f ( x) 
4 x
?
x3  x
a.
D f  x | x  4  (, 4]
b.
Df  x | x  4  (, 4)
c.
Df  x | x  4, x  1,0,1
d.
Df  x | x  4, x  1,0,1
What is the range of the function f ( x) 
1
5?
x2
a.
R f   y | y  5
b.
R f   2,  
c.
R f   y | y  5
d.
R f  (0, )
On which sub-interval(s) of 2,2 is the function f (x)  x 3  3x decreasing?
8.
a.
2,2
c.
2,1 and 0,1
 b.




9.

For the function f (t ) 
values of A and B ?
10.
d.
2,1 and 1,2
1,1


2t  A
, if f (4)  0 and f (1) is undefined, then what are the
tB
a.
( A, B)  (8,1)
b.
( A, B)  (8,1)
c.
( A, B)  (8, 1)
d.
( A, B)  (8, 1)
If ( 2, 6) is a point on the graph of y  f ( x) , then what is the corresponding point on
the graph of y  2 f (3  x) ?
a.
(10, 6)
b.
(5,12)
c.
(1,12)
d.
( 2, 6)
Show all your work on the following problems to receive full credit.
Problem 1
[15 pts]
Consider the circle described by the equation
x2  y 2  6x  4 y  3 .
a)
What is the center and radius of this circle? Show your algebraic work below.
b)
What are the intercepts, if any, of this circle? Use exact forms for all coordinates.
Problem 2
[20 pts]
Let f and g be two functions defined respectively by f ( x)  x  6 and g ( x)  x 2  9 .
Now consider the function h defined by h( x) 
a)

Write h explicitly
as a function of x .
b)
Find Dh , the domain of h .

c)
3  f ( x)
.
g ( x)

6

Does the point  2,   belong to the graph of h ? Justify your answer.
5


d)
Find the x- and y-intercept(s) of the graph of h . Use exact forms.

Problem 3
[20 pts]
Consider the hyperbola described by the equation
y  3
1
.
x4
a)
Using the grids below, plot this curve using a sequence of 3 transformations starting
with the graph of an elementary function. Label 2 points on the initial curve and follow
these points through all stages of the transformation.
b)
What is the range of the function f ( x)  3 
1
?
x4
_________________
Problem 4
[5 pts]
Suppose f is an odd function. Explain why the graph of y  f ( x) is necessarily symmetrical
with respect to the y-axis. Illustrate this property with an example.
Bonus Problem
[5 pts]
Find the slope of the line passing through the centers of the two circles C1 and C2 described
by the following equations:
C1 : x 2  y 2  4 x  6 y  4  0
C2 : x 2  y 2  6 x  4 y  9  0