MATH 142 Business Math II, Week In Review
Spring, 2015, Problem Set 1 (A.8, 1.1, 1.2)
JoungDong Kim
(1-8). Find the domain of each function.
1. f (x) =
2. f (x) =
3. f (x) =
√
2−x
x2
√
4. f (x) = √
x−1
− 5x + 6
x+2
x
x
x−1
1
2 y
1
x
1
5.
2
2
y
1
x
2
6. −1
7. f (x) =
8. f (x) =
√
4
x2 − 9
√
x
x−5
2
(9-10). Evaluate the given function at the given values.
9. f (x) =
10. f (x) =
√
1
1
)
, f (1), f ( 12 ), f (−2), f ( 2 − 1), f (x + 2), f ( x+1
x+1
x−1
, f (1), f (−1), f (x + 1), f (x2 )
x+1
3
(11-12). Graph the indicated function. Find the intervals on which each function is continuous.



 x2
if x ≤ 0
11. f (x) =


 x
if x > 0




x2




12. f (x) =
x






 2x
if x ≤ 0
if 0 < x ≤ 1
if x > 1
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(13-15). Determine the domain of each of the given functions.
x3 − 2
13. 2
x −1
1
14. x 6
1
15. x− 7
5
(16-18). Graph the given functions.
16. y = (x − 1)3 − 2
17. y =
√
x+1−2
18. y = −2(x − 1)2 − 1
6
(19-20). Give an equation for the function associated with the transformed graph.
19. y = f (x) = |x|, vertical stretch by 2, shift down by 3.
20. y = f (x) = x3 , reflect through x-axis, shift down by 3, shift left by 2.
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(21-22). Find the break-even quantitiy.
21. C = 3x + 10, R = 6x
22. C = 0.03x + 1, R = 0.04x
(23-24). Find the equilibrium point.
23. Demand: p = −3x + 12, Supply: p = 2x + 5
24. Demand: p = −0.1x + 2, Supply: p = 0.2x + 1
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25. Find where the revenue function is maximized using the linear demand function p = −2x + 3
26. Find the profit function using the given revenue and cost functions. Find the value of x that
maximizes the profit. Find the break-even quantities: that is, find the value of x for which the
profit is zero.
R(x) = −2x2 + 30x, C(x) = 10x + 42
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27. It is found that the consumers of a particular toaster will demand 64 toaster ovens when the unit
price is $35 whereas they will demand 448 toaster ovens when the unit price is $5. Assuming that
the demand function is linear, and the selling price is determined by the demand function,
a) Find the demand equation.
b) Find the revenue function.
c) Find the number of items sold that will give the maximum revenue. What is the maximum
revenue?
d) If the company has a fixed cost of $1,000 and a variable cost of $15 per toaster, find the
company’s linear cost function.
e) What is the company’s maximum profit?
f) How many toasters should be sold for the company to break even?
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