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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.