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Unformatted text preview: x brackets often take the form of piecewise linear functions. Consider the 2010 U.S. Rate
Schedule for single persons, showing the income tax owed, T , as a function of adjusted income, i. for 0 ≤ i ≤ 8, 375 0.10i
0.15(i − 8375) + 837.50
for 8, 375 < i ≤ 34, 000
T= 0.25(i − 34000) + 4, 681.25 for i > 34, 000
(i) If a single person earns an adjusted income of $30,000, how much income tax would the person
owe? (ii) If a person owes $3000 in income tax, what was their adjusted income? 22. Find the vertex of the parabola
y = 2x2 + 8x − 4.
(i) The x-coordinate of the vertex is
(A) less than -1 (B) between -1 and 3 (D) between 7 and 11 (C) between 3 and 7 (E) more than 11 (ii) The y -coordinate of the vertex is
(A) less than -10 (B) between -10 and -5 (D) between 0 and 5 (C) between -5 and 0 (E) more than 5 23. Graph the function y = 2x2 + 6x − 2 below. Give the values of the x-intercepts, the y -intercept, and
the vertex. x-intercepts:
vertex: 24. Let C (x) = 3x + 4 be the cost to produce x widgets, and let R(x) = −x2 + 8x be the revenue. Answer
parts (i) through (iii)
(i) Graph both functions. Choose the correct graph of both functions below. (ii) Find the minimum break-even quantity.
(A) less than 0.5 (B) between 0.5 and 1.5 (D) between 2.5 and 3.5 (C) between 1.5 and 2.5 (E) more than 3.5 (iii) Find the maximum proﬁt.
(A) less than $0.50 (B) between $0.50 and $1.50 (D) between $2.50 and $3.50 (C) between $1.50 and $2.50 (E) more than $3.50 25. The manager of an 60-unit apartment complex is trying to decide what rent to charge. Experience has
shown that at a rent of $900, all the units will be full. On the average, one additional unit will remain
vacant for each $50 increase in rent.
(i) Let x represent the number of $50 increases. Find an expression for the total revenue from all
rented apartments. (ii) What value of x leads to maximum revenue? (iii) What is the maximum revenue? 26. Graph y = x3 − 7x − 8. Choose the correct graph. 27. Graph the function y = −x4 + 4x3 + 12x + 9. 28. The graph below is the graph of a polynomial. Give the possible degree of the polynomial, and give
the sign (positive or negative) of the leading coeﬃcient. (A) degree 4 with negative leading coeﬃcient (B) degree 4 with positive leading coeﬃcient (C) degree 5 with negative leading coeﬃcient (D) degree 5 with positive leading coeﬃcient (E) None of the above 29. Let y = 3 − 2x
. Answer parts (i) through (iii)
2x + 17 (i) What is the vertical asymptote?
2 (A) x = −1 (B) x = − (D) y = −1 (E) There is no vertical asymptote (C) y = (ii) What is the horizontal asymptote?
2 (A) x = −1 (B) x = − (D) y = −1 (E) There is no horizontal asymptote (C) y = (iii) Graph the function. Choose the correct graph below. 30. Suppose a cost-beneﬁt model is given by
100 − x where x is a number of percent and y is the cost, in thousands of dollars, of removing x percent of a
(i) Find the cost of removing 95% of the given po...
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