MATH 107 FINAL EXAMINATION

MULTIPLE CHOICE

1. Determine the domain and range of the piecewise function.

A. Domain [–2, 2];

B. Domain [–1, 1];

C. Domain [–1, 3];

D. Domain [–3/2, –1/2];

2. Solve:

A. 3

B. 3,7

C. 9

D. No solution

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

A. (−1.3, 1.3)

B. (1, 3)

C. (−∞,−1)and (3,∞)

D. (−2.5, 1)and (4.5,∞)

4. Determine whether the graph of y = 2|x| + 1 is symmetric with respect to the origin,

the x-axis, or the y-axis.

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

not symmetric with respect to the y-axis

5. Solve, and express the answer in interval notation: | 9 – 7x | ≤ 12.

A. (–∞, –3/7]

B. (–∞, −3/7] ∪ [3, ∞) C. [–3, 3/7]

D. [–3/7, 3]

6. Which of the following represents the graph of 7x + 2y = 14 ?

7. Write a slope-intercept equation for a line parallel to the line x – 2y = 6 which passes through the point (10, – 4).

8. Which of the following best describes the graph?

A. It is the graph of a function and it is one-to-one.

B. It is the graph of a function and it is not one-to-one.

C. It is not the graph of a function and it is one-to-one.

D. It is not the graph of a function and it is not one-to-one.

9. Express as a single logarithm: log x + log 1 – 6 log (y + 4)

10. Which of the functions corresponds to the graph?

11. Suppose that a function f has exactly one x-intercept.

Which of the following statements MUST be true?

A. f is a linear function.

B. f (x) ≥ 0 for all x in the domain of f.

C. The equation f(x) = 0 has exactly one real-number solution.

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)?

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

A. g(x) = f (x – 3) + 1

B. g(x) = f (x – 1) + 3

C. g(x) = f (x + 3) – 1

D. g(x) = f (x + 1) – 3

SHORT ANSWER:

13. Multiply and simplify: (7 − 4i)2.

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

14. Solve, and write the answer in interval notation:

15. Water initially at 200° F. is left in a room of temperature 70° F to cool.

After t minutes, the temperature T of the water is given by T(t) = 70 + 130e–0.096t

Find the temperature of the water 10 minutes after it is left to cool. (Round to the nearest degree.)

16. Find the value of the logarithm:

17. Solve: 35x-4 = 9.

18. Suppose $1,900 is invested in an account at an annual interest rate of 6.6% 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 + 20x + 97.

(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.

(a) Which sketch illustrates 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

(a) State the domain.

(b) State the horizontal asymptote.

(c) State the vertical asymptote(s).

(d) Which of the following represents the graph of ?

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

22. Let and .

(a) Find . Show work.

(b) Find the domain of the quotient function . Explain.

23. Points (3, –1) and (7, –9) 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, 2) and (– 6, 8). Write the equation in slope-intercept form. Show work.

25. A salesperson earns a base salary of $1,475 per month and a commission of 8.4% on the amount of sales. If the salesperson has a paycheck of $4,637.60 for one month, what was the amount of sales for the month? Show work

26. Let f(x) = 8×2 – 10 and g(x) = x – 2.

(a) Find the composite function and simplify. Show work.

(b) Find . Show work.

27. Find the exact solutions and simplify as much as possible: 2×2 − 1 = 6x. Show work.

2×2 – 6x – 1 = 0

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 500 donuts are made daily?

(b) How many donuts should be made daily in order to maximize the company’s profit? Show work.

30. Solve: . Show work.

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