Assignment

1. Write as a single logarithm: 6 log x – log y + log 1

2. Write a slope-intercept equation for a line parallel to the line x – 5y = 2 which passes through the point (15, –2).

3. Determine whether the graph of is symmetric with respect to the origin, the x-axis, or the y-axis.

4. The percentage score on a test varies directly as the number of correct responses. Tim answered 26 questions correctly and earned a score of 65%. What would Tim’s percentage score have been if he had answered 32 questions correctly?

5. A bowl of soup at 170F. is placed in a room of constant temperature of 60F. The temperature T of the soup t minutes after it is placed in the room is given by

T(t) = 60 + 110 e – 0.075 t

Find the temperature of the soup 16 minutes after it is placed in the room, rounding off to the nearest degree F.

6. Solve, and express in interval notation: | 5 – 6x | ³ 13.

7. Let f (x) = − 14x + 52.

(a) Find the vertex.

(b) State the range of the function.

(c) On what interval is the function increasing?

8. Points (4, –5) and (6, 3) 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.

b) What is the center of the circle?

c) What is the equation of the circle?

9. Let f (x) = 9x2 + 5 and g(x) = x – 1

(a) Find the composite function ( f o g)(x) and simplify

(b) Find f o g (1)

10. Simplify and find exact solutions

2x2 + 5 = 2x

11. Find the equation for a line which passes through the points (3, –8) and (1, 2). Write the equation in slope-intercept form.

12. Graph 4x + 9y = 36

13. Find solution:

14. Find the value:

15. Consider

a) State the domain

b) Horizontal asymptote

c) Vertical asymptote

16. Suppose $2,000 is invested in an account at an annual interest rate of 8.7% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size?

17. A salesperson earns a base salary of $1,850 per month and a commission of 6.4% on the amount of sales made. If the salesperson has a paycheck of $3,046.80 for one month, what was the amount of sales for the month?

18. Find a formula for the inverse function of

19. Endpoints of the diameter of a circle are (4, –5) and (6, 3)

Simplify answer

a) What is the length of the diameter?

b) What is the center of the circle?

c) What is the equation of the circle?

20. Solve the equation

21. Simplify the equation

22. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P (in dollars) is given by

P(x) = –0.002 + 4.5x – 1500

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?