MATH 110 Review

1
MATH 110 Review

• EXAM 2

2
Jeopardy
Old New Combos Lines Quads Poly Want a Cracker Potpourri
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
3
Potpourri 100

• Explain whether or not the table below represents
  a linear function
• Answer no the rate of change is not constant.

X 1 2 3 4 5
Y 3.0 5.1 7.2 9.3 11.5
4
Potpourri 200

• Consider the polynomial function
• What is the degree of P(x)?
• State the end behavior of P(x)
• State the multiplicity of each zero
• Answer degree 6 y ?-8 as x ?8 -2 has
  multiplicity of 3, 4 has multiplicity of 2, and
  -5 has multiplicity of 1.

5
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

6
Potpourri 400

• A restaurants profit P as a function of the
  number of meals served m is given by the equation
• 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.

7
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
• What is the maximum number of inches a redwood
  can grow in one year?
• Answer 13.5 inches.

8
Poly Want A Cracker 100

• What is the smallest degree the polynomial could
  have?
• What is the sign of the leading coefficient?
• Answer minimum degree 5 lead coefficient
  positive

9
Poly Want A Cracker 200

• Find the equation of a polynomial function with
  the following information
• Negative lead coefficient
• Even degree
• Zeros at -3 (multiplicity 1), 0 (multiplicity 1),
  and 5 (multiplicity 2)
• Answer y -x(x3)(x-5)2

10
Poly Want A Cracker 300

• What is the remainder for the following division
• Answer -x15

11
Poly Want a Cracker 400

• Consider the polynomial function
• 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

12
Poly Want a Cracker 500

• Solve the polynomial equation given below
• Answer

13
Quads 100

• Find the equation of a quadratic with vertex
  (2,-1) and passing through the point (1,3).
• Answer

14
Quads 200

• Rewrite the quadratic function given in standard
  form
• Answer

15
Quads 300

• Find the vertex and intercepts of the quadratic
  function given
• Answer V(-0.1,0.03) intercepts (-0.647,0),
  (0.447,0) and (0, 29/1000)

16
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

17
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.

18
Lines 100

• Write the equation of the line passing through
  (-2,2) and having a slope of -0.5.
• Answer y -0.5x1

19
Lines 200

• Write the equation of the line containing the
  points (2,3) and (5,15)
• Answer y 4x-5

20
Lines 300

• Fill in the table below so that the function is
  linear
• Answer the missing y values in order are 4 and
  0.25. The missing x values in order are 2 and
  4.08.

x -1 0 1.5 3
f(x) 6.5 -1 -3.5 -6.2
21
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

22
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

23
Combos 100

• Given the functions and
• State the domain of (f g)(x)
• Answer 4,8)

24
Combos 200

• Consider the functions and
• State the domain of (f/g)(x)
• Answer (-2,0) U (2,0)

25
Combos 300

• Consider the functions and
• Find
• Answer

26
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
  where r is the radius of the
  slick in feet. At the same time, the radius of
  the slick increases according to the function
  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.

27
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
28
Old New 100

• Given that (3,4) is a point on the graph of f(x),
  which of the following must a point on the graph
  of
• (-6, 2)
• (-6, 8)
• (-1.5, 2)
• (-1.5, 8)

29
Old New 200

• Write the equation of the base graph which has
  been transformed in the following ways first,
  reflected over the x-axis, vertically compressed
  by one-third, shifted right 4 units.
• Answer

30
Old New 300

• 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

31
Old New 400

• Suppose that a function f(x) has a domain of
  -6,4. What will the domain be for the function
  ?
• Answer -16,14

32
Old New 500

• Suppose that a function f(x) has a range of
  -2,1. What will the range be for the function
  ?
• Answer 3,9