Math 1304 -- Review for Test #3
Chapter 3: Polynomial and Rational Functions
Chapter 4: Exponential and Logarithmic Functions
1. Page 216 (13 - 18) Graph y = x3 – 5x2 – 6x by finding the zeroes and using a sign chart.
2. Page 225 (13 – 16, 29 – 34) Use the Remainder Theorem to find f(c) or use the Factor Theorem to
determine if x – c is a factor of f(x).
a. Find f(2) if f(x) = x3 – 3x2 – 7x + 6.
b. Is x – 3 a factor of f(x) = 4x3 – 9x2 – 8x – 3?
3. Page 247 (15 – 24) Use the Rational Zero Theorem to find all zeros for 2x3 – 8x2 + 9x – 9 = 0.
4. Page 237 (1 – 6) ; Page 247 (1 – 10) Find the polynomial with zeroes –1 and 7i and where f(2) = 53.
5. Page 265 (7 – 44) Find the coordinates of all intercepts and holes (if any). Find the equation of all
x2  x  6
asymptotes. Sketch the graph. f ( x)  2
.
x  2x  3
6. Page 312 (13 – 16); Page 348 (21 – 24, 31, 32) Solve each of the following exponential equations
a. 3(3x) + 9(3-x) = 28
b. e2x + 2ex – 15 = 0
7. Page 348 (1 – 4, 11 – 16) Solve each of the following exponential equations
a. e2x = 7
b. 42x+3 = 5
8. Page 336 (17 – 24) Solve each of the following logarithmic equations
a. log x + log (x – 1) = log 4x
b. ln x – ln (x + 6) = ln (x – 1) – ln (x + 2)
9. Page 336 (25 – 34) Solve the following logarithmic equation: log3(x + 3) + log3(x + 5) = 1
10. Page 349 (55, 56)
The amount (in grams) of radium 221 remaining in a sample after t seconds is given by:
N(t) = 10e-.023t. After how many seconds will 2 grams remain?