MULTIPLECHOICE
1. Determine the domain and range of the piecewise function.
A. Domain [-3, 1]; Range [ -1, 3]
B. Domain [-1, 1]; Range [0, 1]
C. Domain [-1, 3]; Range [ -3, 1]
D. Domain [1/ 2, 3/ 2]; Range [0, 1]
2. Solve: √6x +27 = - x
A. -27/ 7
B. 3
C. -3, 9
D. No solution
3. Determine the interval(s) on which the function is increasing.
A. (-∞, -1)
B. (-2, 2)
C. (-4.5, -1) and (2.5, ∞)
D. (-∞, -3) and (1, ∞)
4. Determine whether the graph of y = x2 + 7 is symmetric with respect to the origin, the x-axis, or the y-axis.
A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. symmetric with respect to the origin only
5. Solve, and express the answer in interval notation: |6 - 5x| ≤ 14.
A. (-∞, -8/ 5] ∪ [4, ∞)
B. (-∞, -8/ 5]
C. [-8/ 5, 4]
D. [4, ∞)
6. Which of the following represents the graph of 4x -9y = 36 ?
7. Write a slope-intercept equation for a line parallel to the line x -4y = 6 which passes through the point (12, -3).
A. y = |1/4x| -1
B. y = |1/4x| -3
C. y = 1/4 x -3
D. y = -4x + 45
8. Which of the following best describes the graph?
A. It is a parabola.
B. It is not the graph of a function.
C. It is the graph of a one-to-one function.
D. It is the graph of a function but not a one-to-one function.
9. Express as an equivalent expression: log x + log 1-3 log (y + 1)
A. log ( x + 1)/log (3 y + 3)
B. log (x -3 y -2)
C. log ( x + 1)/log ( y + 1)3
D. log x/ (y + 1)3
10. Which of the functions corresponds to the graph?
A. f (x )= 1+ ex
B. f (x )= 2 + e-x
C. f (x )= 2 -ex
D. f (x )= 2 + ex
11. Suppose that a function f has no x-intercepts.
Which of the following statements MUST be true?
A. The equation f (x)= 0 has no real-number solution.
B. The graph of f is a horizontal line.
C. f (x) > 0 for all x in the domain of f.
D. f is an invertible function.
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)?
A. g(x) = f (x + 1) -2
B. g(x) = f (x -2) + 1
C. g(x) = f (x -1) + 2
D. g(x) = f (x + 2) + 1
SHORT
13. Multiply and simplify: (6 -7i)(1-2i).
Write the answer in the form a + bi, where a and b are real numbers.
14. Solve, and write the answer in interval notation: x + 2/(x -9) ≤ 0.
15. A bowl of soup at 165° F. is placed in a room of constant temperature of 75° F. The temperature T of the soup t minutes after it is placed in the room is given by
T(t) = 75 + 90 e-0.075 t
Find the temperature of the soup 10 minutes after it is placed in the room. (Round to the nearest tenth of a degree.)
16. Find the value of the logarithm: log7.1/49.
17. Solve: 23 x+7= 4 .
18. Suppose $7,500 is invested in an account at an annual interest rate of 2.9% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size?
19. Let f (x) = x2 + 18x + 85.
(a) Find the vertex.
(b) State the range of the function.
(c) On what interval is the function decreasing?
20. Consider the polynomial P(x), shown in both standard form and factored form.
P(x) = 1/2.x4 -9/2.x3 + 21/2.x2 + 1/2.x -15 = 1/2(x+1)(x-2)(x-5)
(a) Which sketch ilustrates the end behavior of the polynomial function?
(b) State the zeros of the function.
(c) State the y-intercept.
(d) State which graph below is the graph of P(x).
21. Let f ( x) = x/(x2 -4)
(a) State the domain.
(b) State the horizontal asymptote.
(c) State the vertical asymptote(s).
(d) Which of the folowing represents the graph of f(x) = x/(x2 -4)
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f (x) = x -7 and g (x) = √(x + 3).
(a) Find f/g . Show work.
(b) Find the domain of the quotient function f/g Explain.
23. Points (6, 1) and (8, -7) are endpoints of the diameter of a circle.
(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.
Show work.
(b) What is the center point C of the circle?
(c) Given the point C you found in part (b), state the point symmetric to C about the x-axis.
24. Find the equation for a line which passes through the points (-3, 9) and (1, 1). Write the equation in slope-intercept form. Show work.
25. Marie, a resident of Metropolis, pays Metropolis an annualtax of $46 plus 2.4% of her annual income. If Marie paid $1,702 in tax, what was Marie's income? Show work.
26. Let f (x) = 8x2 -5 and g(x) = x -1.
(a) Find the composite function ( fog )( x) and simplify. Show work.
(b) Find ( fog ) (-2) . Show work.
27. Find the exact solutions and simplify as much as possible: 5x2 = 6x + 3. Show work.
28. Given the function f (x) = 1/x -2 , find a formula for the inverse function. Show work.
29. Lee's Bakery has determined that when x chocolate cakes are made daily, the average cost per chocolate cake, in dollars, is given by
C(x) = 0.001x2 -0.16x + 10.80
(a) What is the average cost per cake if 40 chocolate cakes are made daily?
(b) How many chocolate cakes should be made daily in order to minimize the average cost per cake? Show work.
30. Solve: (x + 10)/(x + 2) + 32/(x2 -4) = 0 . Show work.