Name:_____________________________________________ Period:____________
A
College Algebra- Spring Final
Make sure algebraic work is organized, legible, and supports your answer.
1. Write the partial fraction decomposition of
2𝑥 2 −𝑥−9
.
𝑥 3 −𝑥
1.__________________________(+5)
2. Write the partial fraction decomposition of
12𝑥+3
.
𝑥 3 −1
2.__________________________(+5)
3. Solve in the complex number system.
𝑥 4 + 10𝑥 = −𝑥 2
4.__________________________(+5)
4. Solve algebraically.
5 1
1
− [𝑙𝑜𝑔3 𝑥 + 𝑙𝑜𝑔3 (𝑥 − 2)] = − 𝑙𝑜𝑔4 4
3 2
3
5.__________________________(+5)
2𝑥 2 +𝑥−3
5. Analyze the graph of the rational function 𝑅(𝑥) = 2𝑥 3 −12𝑥2 +10𝑥.
a. Find the domain.
b. Write 𝑅(𝑥) in lowest terms and identify any holes
in the graph.
c. Locate the intercepts of the graphs.
d. Locate any vertical asymptotes.
e. Locate any oblique or horizontal asymptotes.
Determine if crossed.
f. Identify any potential local maxima or minima.
g. Graph.
a.______________________(+10)
b.______________________
c.______________________
d.______________________
e.______________________
f.______________________