1315 1
2
3
4
5
6
7
8
9
10
Total
MATH Final Exam Instructor: C. Gunning Name: 1. 10 points Solve the following equations: (a) 3x = 9x
3
(b) e2x+5 = 8
(c) log x + log (x + 15) = 2
1
2. 10 points Graph the following polynomials by hand. Show all work! (a) f (x) = -3(x - 5)(x - 1)(x + 2)(x + 4)
(b) g(x) = -2x(x + 2)2
2
3. 10 points A farmer wants to fence three sides of a field with 12,000 feet of fencing. (The fourth side runs along a pre-existing fence.) What dimensions should he fence to give him the maximum area possible?
4. 10 points Determine all the asymptotes (vertical, horizontal, oblique) for the following function. Do not graph! x3 - 1 G(x) = x - x2
3
5. 10 points Perform the indicated exercise: (a) Determine the center and radius of the circle x2 + y 2 - 6x + 2y + 9 = 0.
(b) Find the x and y intercepts of the following circle (x + 1)2 + (y 1)2 - = 2
4
6. 10 points Find the equation of the line with the given properties (put final answer in y = mx + b form): (a) Slope = 3; containing the point (-2, 3)
(b) Containing the points (1, 3) and (-1, 2)
7. 10 points Graph the following quadratic function by hand. Label the vertex and all intercepts. Show all work for credit! f (x) = x2 + 2x - 8
5
8. 10 points The formula D = 5e-0.4h can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug has been administered. When the number of milligrams reaches 3, the drug is to be administered again. What is the time between injections?
9. 10 points Graph the following rational function by hand. Show all work. f (x) = 4x + 2 x - 20
6
10. 10 points Find in class).
f (x + h) - f (x) , for f (x) = x2 -x+4. Be sure to simplify fully (as discussed h
7