1
c
Kathryn
Bollinger, January 21, 2014
Week-In-Review #1 (A.8, 1.0, 1.1 topics, 1.2 topics, 1.3)
1. Classify the following functions as a polynomial function (state its degree and leading coefficient),
power function, rational function, exponential function, or none of these (and explain why not).
(a) h(x) = 4 − x2 −
3
x−4
(b) f (x) = (0.25)x
√
t5t
(c) g(t) = 2
t −9
√
(d) f (x) = 8x5
(e) h(t) =
3t2 − 78t
1 − t9
(f) m(x) = 1 + x3 − 2x1/5 + x2
(g) h(t) = −πt2
2. If f (x) = 2x2 − x, find and simplify
(a) f (−1)
√
(b) f ( 3)
(c) f (∗)
(d) f (a + b)
(e) f (x + h)
(f)
f (x + h) − f (x)
h
f (x + h) − f (x)
.
h
3. If f (x) =
√
4. If f (x) =
x
f (a + h) − f (a)
, find and simplify
.
x+1
h
2x + 3, find and simplify
2
c
Kathryn
Bollinger, January 21, 2014
5. Given the graph of f below to the right, find the following:
(a) f (2)
y
6
(b) Where f (x) = −1
(c) Domain of f
2
(d) Range of f
x
(e) Interval(s) over which f (x) is increasing
2
(f) Interval(s) over which f (x) is decreasing
6. Find the domain of the following functions. Express your answer using interval notation.
(a) f (x) = x10 + 2x5 − πx + 7
x−2
+x−6
√
6−x
(c) g(x) = 2
x − 6x − 16
(b) n(x) =
x2
2x
4x + 9
√
5
x−7
(d) h(x) = √
(e) m(x) =
2
3 x−6
(f) n(x) = 5(2x + 1)−1/3
(g) r(x) =

1




 (x + 3)(x − 8)
, x < −2


2


 √
4
,x≥1
x
(h)
y
6
2
x
2
4
6
4
c
Kathryn
Bollinger, January 21, 2014
3
7. Make an accurate graph of the following and find its domain.


 x
, x ≤ −2
f (x) =
+ 1 , −2 < x < 1

 1
,x>3
x2
8. You are moving across the country for a new job and find out that the moving companies charge
approximately $2 per pound of stuff to be moved. A perk of your new job is that your new employer
will pay all or part of this moving expense, dependent upon how much stuff you have to move.
Your new company will pay 100% of this cost for the first 5000 lbs to move. They will pay 75% of
the next 5000 lbs, and they will not pay for additional costs associated with any weight over 10000
lbs to be moved. If x represents the number of pounds of stuff you have to move, find a piecewise
function describing your moving expenses.
9. If f (x) = x3 and g(x) = −5(x − 2)3 + 4, how was f (x) transformed to get g(x)?
10. A computer bought in Jan. 2000 for $1500 is worth $900 in Jan. 2002.
(a) Assuming the computer’s value depreciates at a constant rate, find the value of the computer
as a function of the number of months since it was purchased.
(b) What will the computer be worth in Jan. 2004?
(c) What is the rate of depreciation of the computer?
c
Kathryn
Bollinger, January 21, 2014
4
11. The price-demand and price-supply equations for a particular brand of fingernail polish are
found to be p = −3x + 12 and p = 2x + 5, respectively. Let x give the number of thousands of
bottles of fingernail polish and p give the price in dollars.
(a) Find the equilibrium point for the market.
(b) Find the number of bottles of fingernail polish that are demanded when revenue is maximized.
12. KB and Co. produces cabinets. It costs KB and Co. a total of $400 to produce 10 cabinets.
It can sell a total of 15 cabinets when they are priced at $85 each and 20 cabinets if the price is
reduced to $60 per cabinet. If KB and Co. decides not to produce any cabinets, they will still have
costs totaling $200. Find
(a) the linear price-demand function.
(b) the linear cost function.
(c) the revenue function.
(d) the profit function.
(e) the break-even point(s) and, therefore, over which intervals KB and Co. will realize a profit
gain or loss.
(f) the profit/loss from selling 10 cabinets.
(g) the price that should be charged in order to maximize the company’s profit.
13. Simplify the following expressions.
√ 7
2x−4 yz
(a) √
( x3 )y −1
(b) (ct+1 d−t )2+t
14. Solve the following for x algebraically. Give your solution as an EXACT answer.
2
2
(a) 125( 3 x+3) =
5(x )
15625
(b) x3 5x − x5x = 0
15. How much money will be in an account after 2 years on a $500 deposit that earns interest at
a rate of 5% per year compounded continuously?
16. If Mark invests $5000 into an account paying interest at a rate of 8% per year compounded
monthly, how much money will he have at the end of 5 years (assuming no additional deposits or
withdrawals)?
17. In 18 months Brian needs $1750 in order to buy a specific computer. If he finds an account
paying interest at a rate of 5.95% per year compounded weekly, how much could he invest now in
order to have the money he needs for the computer?
c
Kathryn
Bollinger, January 21, 2014
5
18. Which account would be a better account for an investment? For a credit card?
OPTION A: 9% per year, compounded monthly
OPTION B: 8.8% per year, compounded daily
OPTION C: 8.9% per year, compounded continuously
19. In 2002, the estimated population of an area was 6.2 million and was known to be growing
continuously at a relative rate of 1.25% a year. Use this information to estimate the population of
the area in 2014.