Math 150
Exam 2 Review
1. Find the center and radius of each circle.
a)
x
2
 y
2
 4x  6y  9
b)
2x
2
 2y
2
 5x  7 y  0
2. Determine whether the given point lies inside, on or outside the given circle.
a)
P (  2 ,5 )
b)
P ( 5,2 )
x
2
 y
2
 3 x  8 y  12  0
A diameter
of the circle
is the line segment
from A(3,4)
to B(1,8)
3. Find the perpendicular bisector of the line segment from A(-3, 7) to B(5, 1).
4. Find the slope intercept equation of the line through (a, f(a)) with the given slope, m.
a)
5.
x
f (x) 
2
1
x  2
 3x

 x 1
f (x)  
 x  2
 2
x  4
a  1
f (x) 
f (x) 
x
2
 9
x  9
x  9
b) Find f(5) and f(12).
g(x)  4  x
x
b)
2
a) Find
g  f
and find its domain.
b) Find
f g
and find its domain.
7. Find the maximum value of :
a)
p( x)  2 x
2
 12 x
b)
q( x)  3x
2
 15 x  12
8. Find the minimum value of :
a)
p(x)  4x
c)
25 ( x  2 )
2
2
a  4
m 
4
5
a) Find the domain of f.
6.
m  2
 8 x  16
 16 ( y  3 )
b)
2
 400
q ( x )  ( 2 x  8 )( 3 x  12 )
9. Test each relation for symmetry about the x-axis, y-axis and origin.
a)
x
2
 y
3
 xy  10
b)
3
x y
3
 x
4
 2
10. Find the domain of each function.
a)
f (x) 
x
2
 5x  6
g(x) 
b)
2
2x  x
11. For each quadratic, find i) the axis of symmetry ii) the maximum or minimum value
of f(x) and iii) list the transformations of y  x 2 that result in f(x).
a)
f ( x )   2 ( x  5 )( x  7 )
f (x)  4x
b)
2
 12 x  6
12. For each polynomial, find the degree, leading coefficient, behavior at
behavior at   .
a)
p( x)  5 x
3
 2 x  40
b)
4x
5
 3x
2
 9
c)
 3x
4
 90 x
3

and
 100 x
13. Find the inverse function to each. Give the domain and range of f and of its inverse.
a)
f (x)  3x
c)
f (x) 
5
2
 6 x  8 on [1 ,  )
2x  1
d)
b)
f (x) 
f (x)  3x
5x
x  3
14. List in a proper order the transformations of
e)
2
 6 x  8 on (   , 1 ]
f (x) 
1
x  7
2
y 
1
that result in:
x
a)
f (x) 
2x  3
x  4
b)
f (x) 
x  5
3x  6
15. Two hundred pounds of fruit are being stored in a refrigeration unit. The quantity is
decreasing by 10 pounds per week due to aging. The current price for the fruit is $1.00
per pound. The price per pound is increasing by $0.25 per week. After how many weeks
will revenue be at a maximum? How do you know it is a max?
16. a) A fence will enclose a rectangular area and have a partition parallel to two sides.
The total amount of fence material is 1200 ft all 6ft high. what is the maximum area that
can be enclosed?
b) Rework a) if one side of the area perpendicular to the partition is the wall of a
building.
c) Rework b) if there is no partition.
17. Sketch p(x) and |p(x)| for each.
a)
p ( x )   2 ( x  1 )( x  1 )( x  3 )
b)
p(x)  3x
c)
p(x)  4  x
18. Simplify
2
 12 x
2
f (x  h)  f (x)
for each.
h
a)
f (x)  4x
2
 2x
b)
f (x) 
1
x