Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 2
1. Classify the following functions as power, polynomial (state its degree and leading coefficient), rational, exponential, or none (state why).
(a) 8x5 − 22x
√
(b) 8x5 − 22 x
1
(c) 3x 2
(d) 3x2
(e)
5x4 −8x3 +22
−2x2 +12x+1
(f) 8x
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
2. Find the domain of the following functions (in interval notation):
(a) 4x2 + 22x3 − 83x + 4π
(b)
5x2 +13x−2
(x−4)(x+4)
(c) e
(d)
√
4
3x−27
8x2
1
(2−x) 8
(e) f (x) =
1
1+x
√
5−x
ex+2
x<2
x≥2
Week 2
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 2
3. Let f (x) = x3 . Write a formula for g(x) where the graph of g(x) is the graph of f (x)
shifted 1 unit right, contracted by 31 , and shifted 2 units down.
4. Let f (x) = x2 − 3x + 4. 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 2
5. Consider the following piecewise defined function: f (x) =
1
x<1
1+x
√
5−x x≥1
(a) Graph the function
6
4
2
0
-2
-4
-6
-4
(b) Calculate f (1).
(c) Calculate f (−1).
(d) Calculate f (−3).
-3
-2
-1
0
1
2
3
4
5
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 2
6. Where is the function y = x3 + 4 concave up?
7. The fixed cost for a company that produces calculators is $1300 with a variable cost of
$74 per calculator. The company sells the calculators for $100 each. Assume cost and
revenue are linear.
(a) What is the cost of making 1100 calculators?
(b) What is the profit function for the company?
(c) How many calculators must the company sell to break even?
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 2
8. A certain model of a new car is worth $51,000 and depreciates in value linearly. According
to automobile product information, the car will have lost all its value in 17 years.
(a) Find the equation that relates the value, V , of the car to the number of years, t,
since purchasing the car new.
(b) How much will the car be worth in 6 years?
9. Market analysis has found that the demand equation for a particular brand of computer
is given by p = 2370−30x, where p is the price per computer in dollars and x is thousands
of computers sold.
(a) What is the revenue function for the company?
(b) What is the maximum revenue (to the nearest dollar)?
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 2
10. (a) In 3 years, Alice wants to have $4500 saved up for a trip around the world. She
finds a bank account with an 8% annual interest rate compounded quarterly. How
much money should she put in the account now in order to fund her trip?
(b) Alice’s friend Becca wants to take the same trip. She puts $3800 in an account
with a 7.8% nominal interest rate compounded continuously. How much money
will Becca have saved up after 3 years?
(c) Using effective yield rates, identify whose account is better for earning money.
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
Week 2
11. A swingset manufacturer’s price-demand function is given by p(x) = −0.3x + 540, where
p is the price in dollars of each swingset when x computers are sold. The company will
not supply any swingsets if the unit price is $250 or lower, and they will supply 375
swingsets if the unit price is $325.
(a) Find the price-supply function for the swingsets, assuming it is linear.
(b) What is the market equilibrium quantity?
(c) What is the market equilibrium cost per swingset?
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
12. Simplify the following expressions without using radicals or negative exponents:
−7 4
(a) xx6 y4
(b)
p
3
x12 y −8
Week 2
Mr. Orchard’s Math 142 WIR
Sections A.8, 1.1-1.3
13. Solve the following equations for x:
(a)
1
85x
= 88x−13
(b) 32x = 96x−6
(c) 78x−13 7x = 1
Week 2