Math 150
In Class Exam 2 Review
1. Find the center and radius of each circle.
a)
3x
2
 3y
2
 6 x  12 y  15
b)
2x
2
 2y
2
 12 x  10 y  8  0
2. Determine whether the given point lies inside, on or outside the given circle.
a)
P (3, 2 )
b)
P (5 ,6 )
x
2
 y
2
 4 x  8 y  12  0
A diameter
of the circle is the line segment
from A(1,5)
to B(3,9)
3. Find the perpendicular bisector of the line segment from A(9, 4) to B(5, 2).
4. Find the slope intercept equation of the line through (a, f(a)) with the given slope, m.
a)
f (x)  3x
1 3
a  8
m 
1
b)
4
5.
 5x  5
 2
 x 1
f (x)  

x
 2
x  4
f (x) 
x
2
a  1
1
x  3
b) Find f(2), f(3)and f(5)
g(x)  4  x
x  5
x
x  3
a) Find the domain of f.
6.
x  5
f (x) 
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)  3x
2
 21 x
q( x)  5x
b)
2
 10 x  12
8. Find the minimum value of :
a)
p(x)  2 x
2
 8 x  20
b)
q ( x )  ( 2 x  10 )( 3 x  15 )
m  5
9. Test each relation for symmetry about the x-axis, y-axis and origin.
a)
x
4
 5y
3
 x
2
y  0
b)
xy
5
 x
3
 0
10. Find the domain of each function.
a)
f (x) 
2
x  5x  6
b)
g(x) 
2x  x
2
c)
2
2
4 ( x  2 )  9 ( y  3 )  36
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 )  3 ( x  10 )( x  8 )
f ( x)  5x
b)
2
 15 x  8
12. For each polynomial, find the degree, leading coefficient, behavior at
behavior at   .
a)
p( x)  6 x
5
 20 x  400
b)
6x
3
 8x
2
 7x
c)
2x  8x
2

 3x
and
6
13. Find the inverse function to each. Give the domain and range of f and of its inverse.
a)
f (x)  2x
c)
f (x) 
3
2
 6 x on [1 . 5 ,  )
x  8
d)
f (x) 
b)
f (x)  3x
x
2x  7
14. List in a proper order the transformations of
e)
y 
2
 12 x  8 on (   , 2 ]
f (x)  5x  3
1
that result in:
x
a)
f (x) 
3x  2
x  5
b)
f (x) 
x 1
3x  9
15. A video game is currently selling for $60 and the store owner can sell 3 per week.
The price is decreasing by $2 per week and sales are increasing by 1 per week. In how
many weeks will his weekly revenue be a maximum?
16. A fence will enclose a rectangular area and have a partition parallel to two sides.
The total amount of fence material is 1600 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. a) Find a polynomial, p(x), with degree 3 and leading coefficient 4 that has roots at
x = -1, x = 2 and x = 7. Sketch (approximately) p(x) and |p(x)|.
b) Find a polynomial, p(x), of degree 3 that has a double root at x=3, a single root at x=5
and has leading coefficient 2.
f (x  h)  f (x)
18. Simplify
for each function.
h
a)
f (x) 
1
x
b)
f (x) 
x
c)
f (x)  x
3