College Algebra Open Response Final Exam Review
1. Given 𝑓(𝑥) = 3𝑥 2 − 2𝑥 determine the average rate of change from 1 to 3.
2. Solve the following logarithm.
log 7 (2𝑥 − 3) + log 7 (2𝑥 − 3) = 2
3. The half-life of radioactive cobalt is 4.9 years. If a sample presently contains 120 grams of
radioactive cobalt now, how much will be present in 50 years?
4. Accurately graph the following function by determining the following: 𝑓(𝑥) =
a) horizontal or oblique asymptote
𝑥 2 −16
𝑥 2 −3𝑥−4
b) write f in lowest terms
c) vertical asymptote(s) and holes
e) domain and range
d) x- and y-intercepts
1
f) additional points
1
5. Determine ALL the complex zeros for the following polynomial.
𝑔(𝑥) = 𝑥 4 − 7𝑥 3 + 14𝑥 2 − 38𝑥 − 60
6. Use the function ℎ(𝑥) = −2(2𝑥 + 4)3 − 3 to answer the following questions.
a) List the transformations.
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b) Graph the function.
c) Determine the domain and range of h(x).
7. Determine the equation for the line in general and slope intercept forms that connect the center of
the two circles.
𝑥 2 + 𝑦 2 + 6𝑥 − 10𝑦 + 28 = 0
8. Solve the inequality
3𝑥−5
𝑥+2
≤ 2.
9. Use the difference quotient,
𝑎𝑛𝑑
𝑥 2 + 𝑦 2 − 14𝑥 − 30𝑦 + 264 = 0
Write your answer in interval notation and graph your solution.
𝑓(𝑥+ℎ)−𝑓(𝑥)
ℎ
, to simplify 𝑓(𝑥) = 𝑥 2 + 5𝑥 − 1.