MATH 109

1
MATH 109

• Exam 3 Review

2
Jeopardy
Quads Log On Potent Potions Pieces of Eight Potpourri
100 100 100 100 100
200 200 200 200 200
300 300 300 300 300
400 400 400 400 400
500 500 500 500 500
3
Quads 100

• Find the focal point and vertical intercept for
  the quadratic function graphed below
• Answer focal pt (3,2.5) vertical int (0,6.5)

4
Quads 200

• Find an equation for the quadratic function
  graphed below in (i) vertex form (ii) factored
  form and (iii) standard form
• Answer

5
Quads 300

• A relief package is dropped from an airplane and
  falls to the ground along a parabolic path
  starting at the vertex of the parabola. The
  package was released when the plane was directly
  above the marker at a height of 5 kilometers, and
  the package hits the ground 4.43 kilometers from
  the marker. If h is the height of the package
  when it is a horizontal distance d from the
  marker, find an equation for h in terms of d.
• Answer

6
Quads 400

• A 5.5 foot tall woman is shooting a free throw.
  The path of the basketball is parabolic in shape
  (see below). The ball reaches a maximum height of
  11.5 feet when the ball is 10 feet horizontally
  from the player. If the ball hits the front of
  the rim, which is 10 feet high, how far is the
  shooter from the front of the rim?
• Answer 15 feet

7
Quads 500

• A skateboard companys profits P(x) are a
  quadratic function of the price x they charge. If
  they sold skateboards for free, they would lose
  37,500. If they charge either 5 or 35, they
  will break even (make no profit). What price
  should they charge per skateboard in order to
  make the most profit, and how much profit will
  they make?
• Answer 20 per skateboard Max profit
  48214.29

8
Log On 100

• Use rules of logarithms to explain how you can
  tell which graph is
• Answer Graph 1 is the thin line graph. Graph 2
  is the thick line graph. Graph 3 is the dotted
  graph. Expand each function with properties of
  logs to see vertical shifts up and down.

9
Log On 200

• Consider the functions
  and Fill in the table below

f(x) g(x)
Domain
Range
Asymptotes
Intercepts
10
Log On 300

• The graphs of two exponential functions of the
  form
• and two logarithmic functions of
  form
• are shown below.
• Which pairs of functions are logarithmic?
• Which pairs of functions are exponential?
• Which exponential function has the largest
  b-value?
• Which logarithmic function has the smallest
  b-value?

11
Log On 400

• A recycling program is to be introduced to a
  local suburb. The cost of introducing such a
  program in thousands of dollars to p of
  residents can be modeled by the logarithmic
  function
  . Sketch a graph of C(p) in an appropriate
  viewing window. What is the vertical asymptote
  and what does it tell you?
• Answer p 100 cost become
• infinitely large as the of
• residents on the program
• approaches 100.

12
Log On 500

• A recycling program is to be introduced to a
  local suburb. The cost of introducing such a
  program in thousands of dollars to p of
  residents can be modeled by the logarithmic
  function
• The budget for the recycling program is 200
  thousand dollars. What percentage of residents
  can be put on the recycling program?
• Answer About 95 of residents

13
Potent Potions 100

• Billys uncle has 17 coins in his pockets and the
  coins are either quarters or dollars. There is a
  total of 8.00 in his uncles pockets, and if
  Billy can find the correct number of each type of
  coin, he gets to keep the 8.00. Help Billy get
  rich.
• Answer 12 quarters and 5 dollars

14
Potent Potions 200

• A new teacher has placed an order for textbooks.
  There are two types of textbooks, algebra and
  trigonometry. The algebra books are 18.50 and
  the trig books are 15. If the teacher orders
  273 textbooks and spends 4536, how many books of
  each type did she buy?
• Answer 126 algebra books 147 trig books

15
Potent Potions 300

• Willow needs a 43 sage powder for her spell. At
  the Magic Shop, she is able to buy a 32 sage
  powder and a 74 sage powder. If she needs 200
  grams of her 43 sage powder, how many grams of
  the two available powders should she buy to make
  the powder for her spell?
• Answer 147.62 grams of the 32 sage powder
  52.38 grams of the 74

16
Potent Potions 400

• Allison has a 32 silver solution and a 73
  silver solution. If she is going to mix the two
  together to get 60 grams of a 46 silver
  solution, how much of the 32 silver solution
  does she need?
• Answer 39.51 grams of the 32 silver solution

17
Potent Potions 500

• Jimmy loves to go to the local burger joint where
  he can mix sodas to make his favorite drink which
  is 63 cola. His brother has already mixed a 6
  ounce drink that is 37 cola. How many ounces of
  pure cola should Jimmy add to get his favorite
  drink?
• Answer 4.22 ounces of pure cola

18
Pieces of Eight 100

• Find a formula for the piecewise function graphed
  below
• Answer

19
Pieces of Eight 200

• ComGas, the Cambridge power company, charges its
  customers 6.56 a month, plus an additional 0.87
  per therm up to 28 therms. Any therms over 28 are
  charged at 0.58 per therm. (A therm is a unit of
  gas supplied). Express the monthly cost as a
  function of the number of therms used.
• Answer

20
Pieces of Eight 300

• A t-shirt printing company charges a set-up fee
  of 10 for each order, plus the cost per shirt as
  shown in the table below
• Express the cost of an order, C, as a piecewise
  function, n, the of shirts ordered.

21
Pieces of Eight 400

• A t-shirt printing company charges a set-up fee
  of 10 for each order, plus the cost per shirt as
  shown in the table below
• Sketch a graph of the cost of ordering up to 40
  t-shirts.

22
Pieces of Eight 500

• The graph below shows a graduated tax system
• Describe the tax system in words. HINT find a
  piecewise function for the graph
• Answer First 45000 of income is taxed at 5.
  The next 50000 of income is taxed at 15, and
  any income over 95000 is taxed at 30.

23
Potpourri 100

• Consider the system of linear equations
• Find the value of A so that the system has no
  solutions.
• Answer A 6

24
Potpourri 200

• Consider a power function of the form
  Suppose p is EVEN and (-1,1)
  is a point on the power function. What can you
  say about k?
• Answer k gt0

25
Potpourri 300

• A radioactive substance has a very long
  half-life. If you have 100 grams of the
  substance now, one year from now there will still
  be 99 grams left. Construct three exponential
  models by completing the table below.

26
Potpourri 400

• Which function approaches zero faster as x goes
  to positive infinity?

27
Potpourri 500

• Which of the following functions transforms the
  graph of left 1 unit and
  reflected over the x-axis?