MATH 110 Review
EXAM 2
Jeopardy
Poly
Want a Potpourri
Cracker
Old &
New
Combos
Lines
Quads
100
100
100
100
100
100
200
200
200
200
200
200
300
300
300
300
300
300
400
400
400
400
400
400
500
500
500
500
500
500
Potpourri 100
• Explain whether or not the table below
represents a linear function:
X
1
2
3
4
5
Y
3.0 5.1 7.2 9.3 11.5
• Answer: no; the rate of change is not constant.
Potpourri 200
• Consider the polynomial function
P  x   2 x  2   x  4   x  5
3
2
• What is the degree of P(x)?
• State the end behavior of P(x)
• State the multiplicity of each zero
• Answer: degree 6 ; y →-∞ as x →±∞; -2 has
multiplicity of 3, 4 has multiplicity of 2, and -5
has multiplicity of 1.
Potpourri 300
• An airplane flies at 80 mph for the first
third of a trip and then 120 mph for the rest
of the trip. The entire trip is 400 miles.
How long does the trip take?
• Answer: 3.75 hours
Potpourri 400
• A restaurant’s profit P as a function of the number of
meals served m is given by the equation
10
P  m  200
3
• State the intercepts and give a practical interpretation for
each. What is the slope of this line? What does this
number tell you about the profit?
• Answer: y-int (0,-200) means profit is -200 dollars; x-int
(60,0) break-even point ; slope is (10/3) meaning every
three meals served, the profit increases by 10 dollars.
Potpourri 500
• A horticulturist has determined that the
number of inches a young redwood tree
grows in one year is a function of the
annual rainfall r given by :
g r   0.02r  r  1
2
• What is the maximum number of inches a
redwood can grow in one year?
• Answer: 13.5 inches.
Poly Want A Cracker 100
• What is the smallest
degree the polynomial
could have?
• What is the sign of
the leading
coefficient?
y



x
        

• Answer: minimum
degree 5 ; lead
coefficient positive













Poly Want A Cracker 200
•
Find the equation of a polynomial
function with the following information:
1. Negative lead coefficient
2. Even degree
3. Zeros at -3 (multiplicity 1), 0 (multiplicity
1), and 5 (multiplicity 2)
•
Answer: y = -x(x+3)(x-5)2
Poly Want A Cracker 300
• What is the remainder for the following
5
4
2
2



x

2
x

3
x

5
x

1

x
 2
division:
• Answer: -x+15
Poly Want a Cracker 400
•
Consider the polynomial function
f x   x 3  2 x 2  4 x  8
•
1.
2.
3.
Which of the following is/are true?
-2 is a zero of f(x)
x – 2 is a factor of f(x)
f(x) has only one real zero
Poly Want a Cracker 500
• Solve the polynomial equation given
below: x 4  x 3  5 x 2  3x  6  0
• Answer:  1,2, 3
Quads 100
• Find the equation of a quadratic with
vertex (2,-1) and passing through the point
(1,3).
2


• Answer: y  4 x  2  1
Quads 200
• Rewrite the quadratic function given in
4 2
standard form: y  5 x  8 x  3
• Answer:
4
2
y   x  5  23
5
Quads 300
• Find the vertex and intercepts of the
quadratic function given:
1 2 1
29
f x    x 
x
10
50
1000
• Answer: V(-0.1,0.03) ; intercepts: (0.647,0), (0.447,0) and (0, 29/1000)
Quads 400
• A box is being constructed by cutting 2
inch squares from the corners of a
rectangular piece of cardboard that is 6
inches longer than it is wide. If the volume
of the box is to be 224 cubic inches, find
the dimensions of the cardboard.
• Answer: 12 inches by 18 inches
Quads 500
• A frame for a picture is 2 inches wide all
around. The picture inside the frame is 4
inches longer than it is wide. If the area of
the picture is to be 320 square inches, find
the outside dimensions of the picture
frame.
• Answer: 20 inches by 24 inches.
Lines 100
• Write the equation of the line passing
through (-2,2) and having a slope of -0.5.
• Answer: y = -0.5x+1
Lines 200
• Write the equation of the line containing
the points (2,3) and (5,15)
• Answer: y = 4x-5
Lines 300
• Fill in the table below so that the function
is linear:
x
f(x)
-1
6.5
0
1.5
3
-1
-3.5 -6.2
• Answer: the missing y values in order are
4 and 0.25. The missing x values in order
are 2 and 4.08.
Lines 400
• Find k so that the line containing the points
(-3,k) and (4,8) is parallel to the line
containing the points (5,3) and (1,6).
• Answer: k = 13.25
Lines 500
• On most state highways, the fine for speeding
depends on the speed of the car. In a certain
state where the speed limit is 65 mph, the fine
for driving 70 mph is $30 and the fine for driving
85 mph is $90. Assuming this relationship is
linear, find the equation of the line that
expresses the fine as a function of the speed of
the car. How fast do you need to be driving to
be fined $110?
• Answer: Equation: y = 4x-250 ; 90 mph
Combos 100
• Given the functions f x   6  x and
g x   x  4
• State the domain of (f + g)(x)
• Answer: [4,∞)
Combos 200
1
• Consider the functions f  x   and
x
g x   4  x 2
• State the domain of (f/g)(x)
• Answer: (-2,0) U (2,0)
Combos 300
2


f
x

x
 6 and
• Consider the functions
g x   4 x  1
• Find  f  g x 
• Answer:
16 x  8 x  5
2
Combos 400
• An accident at an oil drilling platform is causing a circular
shaped oil slick to form. The volume of the slick is
roughly given by V r   0.08r 2 where r is the radius
of the slick in feet. At the same time, the radius of the
slick increases according to the function rt   0.5t
where t is in minutes.
• Find V(r(t)) and give a practical interpretation
• How long until the volume of the slick is 226 cubic feet.
• Answer: V(r(t)) tells us the volume of the slick t minutes
after it started. It takes about an hour for the slick to
reach 226 cubic feet.
Combos 500
• Find f(g(2)) and g(f(0)) given the tables below:
• Answer: 3 ; 1
x
f(x)
g(x)
0
2
2
1
3
2
2
1
1
Old & New 100
•
Given that (3,4) is a point on the graph of
f(x), which of the following must a point
1
on the graph of y  f  2 x 
2
a)
b)
c)
d)
(-6, 2)
(-6, 8)
(-1.5, 2)
(-1.5, 8)
Old & New 200
2
y

x
• Write the equation of the base graph
which has been transformed in the
following ways: first, reflected over the xaxis, vertically compressed by one-third,
shifted right 4 units.
• Answer:
1
2
y   x  4
3
Old & New 300
•
•
y  9  x2
Consider the function
. What is
the equation of the graph that will
compress the graph horizontally by a
factor of 3, move the graph left 2 units
and reflect the graph over the x-axis (in
that order).
Answer:
y   9  9x  2
2
Old & New 400
• Suppose that a function f(x) has a domain
of [-6,4]. What will the domain be for the
1



y


f
x

2

 ?
function
3


• Answer: [-16,14]
Old & New 500
• Suppose that a function f(x) has a range of
[-2,1]. What will the range be for the
1 
y


2
f
function
 x  5?
2 
• Answer: [3,9]