A+ Answers
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1. Determine the domain and range of the piecewise function. Show work.
A. Domain [–3, –1]; Range [0, 2]
B. Domain [–2, 2]; Range [–3, 1]
C. Domain [–1, 1]; Range [–2, 0]
D. Domain [–3, 1]; Range [–2, 2]
2. Solve: Show work.
A. No solution
B. –9
C. –9, 3
D. 27/5
3. Determine the interval(s) on which the function is decreasing. Show work.
A. , 1and 5,
B. (1, 5)
C. (– 0.5, 3)
D. (3, 6.5)
4. Determine whether the graph of y 5|x| is symmetric with respect to the origin,
the x-axis, or the y-axis. Show work.
A. symmetric with respect to the origin only
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin
5. Solve, and express the answer in interval notation: | 9 – 7x | 5. Show work.
A. [4/7, )
B. (–, 2] [4/7, )
C. [4/7, 2]
D. (–, 4/7] [2, )
6. Which of the following represents the graph of 4x + 7y = 28? Show work.
7. Write a slope-intercept equation for a line parallel to the line x – 4y = 6 which passes through the point (12, –3). Show work.
8. Does the graph below represent a function and is it one-to-one? Show work.
A. It is not a function but it is one-to-one.
B. It is not a function and it is not one-to-one.
C. It is a function and it is one-to-one.
D. It is a function but not one-to-one.
9. Express as an equivalent expression: log (x – 3) – 8 log y + log 1 Show work.
10. Which of the functions corresponds to the graph? Show work.
11. A candidate’s share of the votes varies directly as the number of votes cast for the candidate. In a city council election with four candidates, Upton received 756 votes and earned a 28% share of the votes. Dillon received 1,080 votes. What was Dillon’s corresponding share of the votes? Show work.
A. 40%
B. 59%
C. 60%
D. 72%
12. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f (x)? Show work.
A. g(x) = f (x – 1) + 2
B. g(x) = f (x + 1) + 2
C. g(x) = f (x – 2) + 1
D. g(x) = f (x + 2) + 1
13. Multiply and simplify:
Write the answer in the form a + bi, where a and b are real numbers. Show work.
14. Solve, and write the answer in interval notation: Show work.
15. Water initially at 200F. is left in a room of temperature 70F to cool.
After t minutes, the temperature T of the water is given by T(t) = 70 + 130e– 0.096 t
Find the temperature of the water 15 minutes after it is left to cool. (Round to the nearest degree.) Show work.
16. Find the value of the logarithm: Show work.
17. Solve: 36x7 9. Show work.
18. Suppose $2,200 is invested in an account at an annual interest rate of 4.2% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Show work.
19. Let f (x) = x2 + 12x + 37. Show work.
(a) Find the vertex.
(b) State the range of the function.
(c) On what interval is the function increasing?
20. Consider the polynomial P(x), shown in both standard form and factored form. Show work.
(a) Which sketch illustrates the end behavior of the polynomial function?
(b) State the y-intercept.
(c) State the zeros of the function.
(d) State which graph below is the graph of P(x).
21. Let . Show work.
(a) State the domain.
(b) State the horizontal asymptote.
(c) State the vertical asymptote(s).
(d) Which of the following represents the graph of Show work.
22. Simplify: Show work.
23. Points (–5, 2) and (3, 6) are endpoints of the diameter of a circle. Show work.
(a) What is the length of the diameter? Give the exact answer, simplified as much as possible. Show work.
(b) What is the center of the circle?
(c) What is the equation of the circle?
24. Find the equation for a line which passes through the points (–3, 8) and (–1, 2). Write the equation in slope-intercept form. Show work.
25. Jim, a resident of Metropolis, pays Metropolis an annual tax of $50 plus 2.1% of his annual income. If Jim paid $1,877 in tax, what was Jim’s income? Show work.
26. Let f (x) = 8x2 – 5 and g(x) = x – 1.
(a) Find the composite function (f ° g)(x) and simplify. Show work.
27. Find the exact solutions and simplify as much as possible: 4x2 + 25 = 16x. Show work.
28. Given the function , find a formula for the inverse function. Show work.
29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P (in dollars) is given by
(a) What is the company’s profit if 800 donuts are made daily?
(b) How many donuts should be made daily in order to maximize the company’s profit? Show work.
11 years ago
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