College Algebra Final Exam Review Assignment # 3
1. Use the properties of logarithms to find the exact value of the expression:
log 8 64 + log 4 192 − log 4 3 − log 9 9
2. Solve the following inequality:
4𝑥 + 10
≥6
𝑥+4
3. Use the polynomial function 𝑓(𝑥) = 𝑥 2 (𝑥 − 2)(𝑥 + 2) to answer the following questions:
a. Find the degree of the polynomial and determine the end behavior.
b. Find the x and y intercepts for the graph. For each x-intercept, determine whether the graph touches
or crosses the x axis.
c. Graph the polynomial with 2 additional points.
4. Write as the sum and/or difference of logarithms. Combine any like terms.
𝑥 2 + 2𝑥
log ( 2
)
(𝑥 − 𝑥 − 6)3
5. Solve algebraically.
1 1
2
− [log 4 𝑥 + log 4 (𝑥 − 6)] = − log 6 6
3 3
3
6. Find all the zeros of the polynomial function 𝑓(𝑥) = 𝑥 3 − 8𝑥 2 + 25𝑥 − 26
7. The half life of Magnesium-27 is 9.45 minutes. If a sample contains 30 grams of Magnesium-27, how
much will be present after 20 minutes.
8. Graph the rational function:
2𝑥 2 − 5𝑥 + 2
𝑓(𝑥) =
𝑥2 − 4