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1. 5

2. –2, 5

3. –2

4. No solution

3. Determine the interval(s) on which the function is decreasing. 3. ______

1. (–∞, –2) and (4, ∞)

1. (–3.6, 0) and (6.7, ∞)

1. (–1, 3)

1. (–2, 4)

the x-axis, or the y-axis. 4. ______

A. symmetric with respect to the x-axis only B. symmetric with respect to the y-axis only

1. symmetric with respect to the origin only

2. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin

1. Solve, and express the answer in interval notation: | 7 – 8x | ≥ 9. 5. ______

1. 1. (–∞, −1/4] ∪ [2, ∞)

   2. (–∞, –1/4]

   3. [–1/4, 2]

   4. [–1/4, ∞)

1. Which of the following represents the graph of 9x − 4y = 36 ? 6. ______

1. 1. B.

C. D.

1. Write a slope-intercept equation for a line parallel to the line x – 3y = 8 which passes through

   the point (– 12, 7).

   7. ______

   1. y =− + x 3

1. 1. y =− −3x 29

1. 1. y = + x 7

1. 1. y = + x 11

1. Does the graph below represent a function and is it one-to-one? 8. ______

1. 1. It is a function but not one-to-one.

   2. It is a function and it is one-to-one.

   3. It is not a function and it is not one-to-one.

   4. It is not a function but it is one-to-one.

2. Express as a single logarithm: log x – 3 log y + log 1 9. ______

1. 1. log(x+ −1 3y)

 x +1

1. 1. log 3 



 x +13

1. 1. log 

 y 

 x  D. log 3 

 y 

1. Which of the functions corresponds to the graph? 10. ______

1. 1. f x( )=− +ex 3

   2. f x( )= e−x +4

   3. f x( )= e−x +3

   4. f x( )= +ex 4

1. Suppose that for a function f , the equation f (x) = 0 has exactly two real-number solutions.

Which of the following statements MUST be true? 11. ______

1. 1. f has exactly two x-intercepts.

   2. f has exactly two y-intercepts.

   3. f is an invertible function.

   4. f is a quadratic function

1. 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)?

12. ______

y = f (x) y = g(x)

1. 1. 1. 1. g(x) = f (x + 1) – 2

         2. g(x) = f (x + 1) – 1

         3. g(x) = f (x + 2) + 2

         4. g(x) = f (x – 1) – 2

SHORT ANSWER:

1. Multiply and simplify: (6 − 5i)(9 + i).

Write the answer in the form a + bi, where a and b are real numbers. Answer: ________

x +1

1. Solve, and write the answer in interval notation: ≤ 0. Answer: ________ x −8

1. Water initially at 190° F. is left in a room of temperature 70° F to cool. – 0.096 t

After t minutes, the temperature T of the water is given by T(t) = 70 + 120e

Find the temperature of the water 20 minutes after it is left to cool. (Round to the nearest tenth of a degree.)

Answer: ________

 1  16. Find the value of the logarithm: log2  . Answer: ________  64 

1. Solve: 57 4x− = 25. Answer: ________

1. Suppose $9,700 is invested in an account at an annual interest rate of 3.2% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in

size? Answer: ________

1. Let f (x) = x2 + 12x + 39.

1. 1. Find the vertex. Answer: ________

1. 1. State the range of the function. Answer: ________

1. 1. On what interval is the function increasing? Answer: ________

1. Consider the polynomial P(x), shown in both standard form and factored form.

P x( ) = x3 −3x2 − + =x 3 (x +1)(x −1)(x −3)

1. Which sketch illustrates the end behavior of the polynomial function?

Answer: ________

1. State the zeros of the function. Answer: ________________

1. State the y-intercept. Answer: ________________

1. State which graph below is the graph of P(x). Answer: ________

GRAPH A GRAPH B

GRAPH C GRAPH D

3x2 +3

1. Let f x( ) = 2 . x −4

1. 1. State the domain. Answer: _________________

1. 1. State the horizontal asymptote. Answer: _________________

1. 1. State the vertical asymptote(s). Answer: _________________

3x2 +3

1. 1. Which of the following represents the graph of f x( ) = 2 ? Answer: ______________ x −4

SHORT ANSWER, with work required to be shown, as indicated.

1. Let f (x) = 5− x and g(x) = x + 2.

1. Find  gf (−4). Show work.

f

1. Find the domain of the quotient function . Explain. g

23. Points (2, –5) and (10, –1) are endpoints of the diameter of a circle.

1. What is the length of the diameter? Give the exact answer, simplified as much as possible. Show work.

2. What is the center point C of the circle?

3. Given the point C you found in part (b), state the point symmetric to C about the x-axis.

1. Find the equation for a line which passes through the points (7, 5) and (4, –1) . Write the equation in slope-intercept form. Show work.

1. A salesperson earns a base salary of $1,960 per month and a commission of 6.8% on the amount of sales. If the salesperson has a paycheck of $4,197.20 for one month, what was the amount of sales for the month? Show work.

1. Let f (x) = 4x2– 7 and g(x) = x + 5.

1. Find the composite function( f οg)( )x and simplify. Show work.

2. Find ( f o g)(−2). Show work.

1. Find the exact solutions and simplify as much as possible: 5x2 + 12 = 20x. Show work.

1. Given the function f x( ) = x −8, find a formula for the inverse function. Show work.

1. The Travel Time bus company has determined that when x tourists are given a particular bus tour, the profit P (in dollars) is given by

P(x) = –0.25 x2 + 28.50x – 300

1. What is the company’s profit if 42 tourists are given the tour?

1. How many tourists should be given the tour in order to maximize the company’s profit? Show work.

x +13 84

30. Solve: + = 0. Show work.

x +6 x2 −36