# A College Algebra Name: _________________________________________

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```College Algebra
Cumulative Final Exam
A
Name: _________________________________________
Period _____________
Open Response: Show all work and reasoning to receive full credit.
CALCULATOR ALLOWED
2𝑥 2 +𝑥−3
1) Accurately graph the following function 𝑓(𝑥) = 2𝑥 3 −12𝑥 2 +10𝑥 by determining the following:
a) horizontal or oblique asymptote
b) write f in lowest terms
c) vertical asymptote(s) and holes
e) domain and range
d) x- and y-intercepts
f) additional points
A
2) Determine ALL real and complex zeros of the polynomial f(x). No decimals.
f ( x)  x 4  2 x 3  22 x 2  50 x  75
3) Find the equation of the line in slope intercept form that connects the centers of the two given circles.
𝑥 2 + 𝑦 2 − 8𝑥 − 6𝑦 + 1 = 0
𝑎𝑛𝑑
𝑥 2 + 𝑦 2 + 12𝑥 − 10𝑦 + 3 = 0
4) Solve the logarithm algebraically.
log15 (𝑥 + 1) + log15 (𝑥 + 3) = 1
A
5) Consider the function 𝑓(𝑥) = −3√𝑥 + 4 + 6..
a) Describe and list the sequence of transformations of the function.
1
1
b) Graph the function on the coordinate plane. 
c) Determine the domain of the function and write using interval notation.
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