1. Express as a single logarithm: log (x2 +3) – 4 log y + log 1

2. The percentage score on a test varies directly as the number of correct responses. Mike answered 39 questions correctly and earned a score of 65%. What would Mike’s percentage score have been if he had answered 45 questions correctly?

3. Points (–6, 1) and (4, 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. Show work.

(b) What is the center of the circle?(c)What is the equation of the circle?

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

5. Ron, a resident of Metropolis, pays Metropolis an annual tax of $60 plus 1.8% of his annual income. If Ron paid $1,032 in tax, what was Ron’s income? Show work.

6. Let f (x) = 6x2 + 5 and g(x) = x – 2.(a) Find the composite function ( f o g)(x) and simplify. Show work.(b) Find ( f o g ) (−1) . Show work.

7. Find the exact solutions and simplify as much as possible: 8x2 + 13 = 20x. Show work.

8. Given the function f (x) = 1

x − 8 , find a formula for the inverse function. Show work.4

9. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P is given by

P(x) = –0.001 x2

+ 2.9x – 1000

(a)What is the company’s profit if 900 donuts are made daily?

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

x +10 3210. x +

2

+ = 0 . Show work. X2 – 4

11. Solve, and express the answer in interval notation: | 8 – 5x | ≤ 12.

12. Determine whether the graph of y = x – 5 is symmetric with respect to the origin, the x-axis, or the y-axis.

A. symmetric with respect to the x-axis onlyB. symmetric with respect to the y-axis onlyC. symmetric with respect to the origin onlyD. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin