Math 142
Week in Review
Set of Problems
Week 2
1) Given the price demand function is p = 3x + 12 and the fixed cost is $288 and the variable
costs are $24. Find the break-even point(s).
2) Which of the following are polynomials?
a. 3x−2 + 4x − 12
b. π x3 + 4x − 2
c. 4 √x + 5
d.(2x + 10) / (x − 5)
3).Solve for x:
a. 8x+2 = 165−x
b. 25 5x = 53x+4
4)
If t represents the time in hours spent studying for the exam, and the average score is
described by the function N = 25(4 − 3e−01t.).
a. If a student does not study, what does this model predict their score will be?
b. If the time spent studying approaches to infinity (or seems like it), what does this model
predict their score will be?
5) Star Bank offers 6% interest compounded monthly, and Bank of Tomorrow offers
continuously compounded interest at 5.75%. If you invest $3000 for 5 years, what would be the
account balance in each bank, assuming no withdrawals?
6) Describe the graph of each of the following functions as related to it’s parent graph.
a. f(x) = x2 − 4
b. g(x) = √(x − 2) − 6
c. h(x) = −2 | x + 1 | + 7
7)
Graph
/
|
f(x) = |
|
\
2
2x −9
, if -3 ≤ x < -1
4x2
, if -1 ≤ x < 2
 20x9
, if 2 ≤ x
8) Evaluate each of the following using the piece-wise defined function above.
a. f(−2)
b. f(4)
c. f(2)
d. f(−3)
9) ax2 + bx + c = a(x − h)2 + k when changed to vertex form. What are the values of h and k?
10) Given: p(x) = 3600−20x where p(x) is the wholesale price in dollars at which x hundred
TV's can be sold, and R(x) is in hundreds of dollars.
a. Find the quantity the company needs to sell to maximize revenue.
b. What is the maximum revenue?
c. What price maximizes revenue?
d. What is the domain?
11)
Finding the domain of the function
2
a) f x =  3 x − 4x1
b) f x = 18 −3x
c) f x =∣x∣
d) f x =  x 5
x1
3
e) f x =  x1
f) f x =  9 −3x
x3
12) Find the average rate of change between the following sets of points:
a. (−5,−3) and (1, 3)
b. (c, d − 1) and (c − 1, d + 1)
13)
Write the equation of the line passing through the point (3,−1) that:
a. has an x-intercept of 2.
b. that passes through the origin.
c. that is horizontal.
14) Plasma TVs of 42” are priced for $1400 and sold 22. The following weekend they moved
the price to $1375 and sold 25. Find a price-demand function which fits this model.
15) A new Laptop costs $300 and in 2 years is worth $250.
a. What is the equation for this depreciation function, assuming it is linear?
b. What is the value of the Laptop in six years?
c. What is the life expectancy of this machine?
16) Silver Company XYZ makes CD players for $150 each, pays rent of $800 per month, $100
per month for utilities and $2400 per month in salaries. If the CD players sell for $280 each,
find:
a) cost equation
b) revenue equation
c) break even point
d) profit or loss when 2000 CD players are made and sold each month.
17)
The amount spent annually in college bookstores in the U.S. is modeled by
f(x) = 0.25 x + 1.3
where x is the number of years since 1982, and f(x) is the amount spent in billions of dollars.
a. How much is the spending increasing each year?
b. According to this model, how much was spent in 1990?
2
18) Given f x = x −6x8 , find and simplify
f  xh− f  x
h
19)
Given: 4x + 2y = 30. If x increases 3a, how is the y value changed?
20) Given p(x) = 106 − .50x and variable costs are $60/unit and fixed costs are $61.80.
a. Find the cost equation.
b. Find the revenue equation.
c. Find the profit equation.
d. Find the break even point.
x
x
2
x
21)
Solve
125 4x 5 − x 5 =0
22)
Solve
125 =5
x
5−2x
23) Jim is saving for a trip abroad after graduation with an account at National Bank, which
pays 13% compounded quarterly. How much does she need to deposit, to reach her goal of
$15, 000 in 54 months?
24) Which of the following functions has an inverse
a) f x =3  x−4
b)
g x =5∣x −2∣ , x > 0.
c)
h x =−2x
3
24
25)
Write in expanded form with no products or quotients:
26) Simplify e
log
x y
4
wz
2lnx3ln x 2
27) Solve for x :
loga  x3log a x =loga 18
28) What is the domain and range of f(x) = 4 + log(x − 3)
3x
29) Solve for x : 4 2 =40
30) Solve for x:
log1 / 3 x −5 =2 log1/ 3  x−3
31) Find the average rate of change for f(x) = 3x2 − x + 5 when x = 1 and ∆x = 3.
32) Solve the following double inequality 2x−4≤365x11
33) Supply and Demand :
Year
Supply
Demand
1990
1995
250
275
300
275
Price in dollars
125
150
a. Find a linear price-supply equation.
b. Find a linear price-demand equation.
c. Find the equilibrium price.
34) Match each item in Column A with the closest description in column B.
Column A
Column B
1. f(x) = x2
a. shaped like a ”v”
2. g(x) = 3√x
b. increasing function,
concave up
c. parabola which opens up
3. h(x) =| x |
4. F(x) = 2x
5. G(x) = √x
d. increasing function,
concave down
e. linear function
6. H(x) = x
f. none of these
35) Graph the piece-wise defined function
/
|
g(x) = |
|
\
−3x16
2
x −2
, if x ≤ 3
, if x > 3
36) Write a function to represent the cost of x items when the store sells the items at $8 each if
you buy less than four items, and charges $2.50 each for additional items up to ten. Let x
represent the number of items purchased.
37) Write in vertex form: f(x) = 3x2 − 12x + 2.
a. Find the domain of f(x).
b. Find the range of f(x).
38) Given: g(x) = -2(x + 5)2 + 10
a. Find the x-intercept.
b. Find the y-intercept.
c. Find the axis of symmetry.
39) Find the equation of the parabola which opens up and has a vertex at (2,−3), and passes
through the point (4, 1).
40) Solve 3 x 1 = 1
11x
28
2
3
3