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MTH 111 – College Algebra Exam 4 - FINAL, Part 2

Name ______________________

Student ID ______________________

Print and answer all of the following questions in your own handwriting. Do not type your answers, but be sure your answers are legible. When completed, scan as a PDF document, and upload through Moodle by THURSDAY, August 20 at 9:55pm Eastern time. No late submissions will be accepted. This part of the exam is worth 70 of the 150 points possible for Exam 4. Each question is worth 10 points.

ALL WORK MUST BE SHOWN TO RECEIVE FULL CREDIT. Unsupported answers will not receive credit. Please clearly mark your final answer.

1. Factor completely: 3𝑥 − 10𝑥 − 8

2. Let 𝑓(𝑥) = 𝑥 + 2 𝑖𝑓 𝑥 ≤ 1

− 𝑥 + 1 𝑖𝑓 𝑥 > 1

a. Evaluate 𝑓(0), 𝑓(−2) and 𝑓(1).

b. Sketch the graph of 𝑓.

MTH 111 – College Algebra Exam 4 - FINAL, Part 2

Name ______________________

Student ID ______________________

3. Solve the system: 𝑥 + 2𝑦 + 𝑧 = 3 𝑦 − 𝑧 = −4 −𝑥 − 2𝑦 + 3𝑧 = 9

4. Consider the polynomial function 𝑃(𝑥) = 𝑥 − 𝑥 − 9𝑥 + 9. Respond to the following statements.

a. Determine the domain of 𝑃(𝑥). b. Determine the end behavior of the graph 𝑦 = 𝑃(𝑥). c. Find the 𝑦-intercept of the graph of 𝑃(𝑥). d. Find all zeros of 𝑃(𝑥), along with their multiplicities. e. Construct a coordinate plane and sketch the graph of 𝑃(𝑥).

MTH 111 – College Algebra Exam 4 - FINAL, Part 2

Name ______________________

Student ID ______________________

5. Given any rational polynomial, say 𝑅(𝑥) = ( )

( ) , write a short paragraph explaining how one

determines the 𝑥-intercepts and the asymptotes of its graph 𝑦 = 𝑅(𝑥).

6. A soft-drink vendor at a popular beach analyzes sales records and finds that if 𝑥 cans of soda are sold in one day, then profit (in dollars) from soda sales is given by 𝑃(𝑥) = −0.001𝑥 +

3𝑥 − 1800. What is the maximum profit per day, and how many cans must be sold to produce this maximum profit?

7. FunTime Carnival wishes to increase the height of their drop-tower attraction to 100 meters, expecting that the additional height will attract more customers. However, state regulations insist that the ride’s average free-fall speed may not exceed 20m/s. Supposing that the ride’s height above ground after 𝑡 seconds is modeled by 𝑠(𝑡) = −4.9𝑡 + 100, determine if FunTime Carnival is behaving ethically with respect to state regulations in their attempt to increase profit.