Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 1
1. Classify the following functions as power, polynomial (state its degree and leading coefficient), rational, exponential, or none (state why).
8
(a) f (x) = 5x 5
(b) y = −2x8 + 3x7 − 12x2 + 33
(c) y(t) = 1000e(.03t)
(d) h(x) =
√
12x13 −4 x+15
5
3x −12x+55
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.5
(e)
(f) y =
8x2 −3x
12x500 −80x300 +30x200 +3x
1
1.5
2
2.5
3
3.5
4
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 1
2. Find the domain of the following functions (in interval notation):
(a) f (x) = x3 − 5x + 23π
3
(b) y = x 4
(c) f (x) =
10x
x2 +10x+9
(d) g(x) = 10
√
5
√
x− 6 x
10
8
6
4
2
0
-2
-4
-6
-8
-10
-6
-4
(e)
(f) h(x) =



x+2
e3x−7
√x
x−1
x−3
2
x −9
x ≤ −1
−1 < x < 1
x≥1
-2
0
2
4
6
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
3. Consider the following function: f (x) =
Week 1
x2 − 6 −2 ≤ x < 1
4
x≥3
(a) Graph the function
6
4
2
0
-2
-4
-6
-4
-3
-2
-1
0
1
2
(b) What is the domain of the function? (Use interval notation.)
(c) Calculate f (−1).
(d) Calculate f (8).
(e) Calculate f (2).
3
4
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 1
4. Let f (x) = |x|. Write a formula for g(x) where the graph of g(x) is the graph of f (x)
shifted 2 units right, contracted by 14 , and shifted 3 units down.
5. Let f (x) =
2
.
3x−7
Calculate the following:
(a) f (a)
(b) f (a + h)
(c) f (a + h) − f (a)
(d)
f (a+h)−f (a)
h
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 1
6. A company makes doodads, and sells them for $28 a piece. When they make 13 doodads,
their cost is $421. When they make only 3 doodads, the cost is $251.
(a) What is the cost function for the company? (You may assume the cost is linear.)
(b) What is the revenue function for the company? (You may assume the revenue is
linear.)
(c) What is the profit function for the company?
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 1
7. According to marketing research done for Time Machine Manufacturer, Inc (TMM), 400
units will be demanded if the price is $260 per time machine. If the price jumps to $360
per unit, only 320 units will be demanded. It costs $240 to build each time machine,
and $4,000 each month in other costs.
(a) What is the monthly cost function for TMM, assuming it is linear?
(b) What is the demand function for TMM, assuming it is linear?
(c) What is the revenue function for TMM?
(d) How many time machines should they manufacture in order to maximize revenue?
What is the maximum revenue?
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 1
(e) What is the profit function for TMM?
(f) How many time machines should they manufacture in order to maximize profit?
What is the maximum profit?
(g) How much should TMM charge for each time machine to maximize profit?
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 1
8. Suppose I put $2500 into a bank account with an annual interest rate of 4.4%, compounded weekly. How much money would I have in the account after 3 years?
9. Bill put $3600 into his bank account 4 and a half years ago. The account was continuously
compounded at a yearly rate of 3.8%. How much money does he have in the account
now?
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 1
10. A manufacturer of laptops found the following set of supply and demand equations where
price is p and x is number of laptops supplied/demanded (in thousands).
(1) p = −3
x + 345
5
(2) p = 52 x + 303
(a) Which equation is the supply equation?
(b) Which one is the demand equation?
(c) What is the equilbrium point? (Round to the nearest whole number or cent.)
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 1
11. (a) Bruce Wayne is saving up to buy a $50 million bat-company. He has a bat-account
with continuously compounded bat-interest at an annual bat-rate of 5.2%. How
much money should he put into his bat-account now in order to have the money 5
years from now?
(b) Alfred suggests to Bruce that he should put his money in a different bat-account,
compounded every bat-quarter at an annual bat-rate of 5.5%. Compare effective
bat-rates to determine if Bruce should take Alfred’s suggestion.
(c) How much money does Bruce Wayne save by going with the better bat-account?
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
12. Simplify the expression leaving no negative exponents:
Week 1
3x2 y −3
x−4 z 3
−2
13. Solve the following equations for x:
(a) 52x−1 5x =
1
25x
(b) 4x x2 − 4x+1 = 0
14. The small (fictional) country of Wakanda had a population of 50,000 in 2010. If it has
a relative population growth of .15% per year, what will the population be in 2020?
(Round to the nearest integer if necessary.)