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MTH 111 College Algebra Exam 3, Part 2

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Student ID ______________________

Print and answer all of the following questions in your own handwriting. Be sure that all answers are legible. Typed submissions will not be accepted. When completed, scan as a PDF document (apps are available for this), and upload through Moodle by the due date listed. No late submissions will be accepted. This part of the exam is worth 25 of the 100 points possible for Exam 3.

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

1. Given the function 𝑓(𝑥) = |𝑥|, apply the following transformations in order, giving the resulting equations for each transformation. Be sure to indicate your final equation. Graph each step of the transformation separately on the same graph. Be sure to indicate the final graph.

a. Shrink vertically by a factor of ½. b. Shift 2 units to the right. c. Shift downward 1 unit.

2. A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 45 cm/s.

a. Find a function 𝑔 that models the radius as a function of time. b. Find a function 𝑓 that models the area of the circle as a function of the radius. c. Find 𝑓 ∘ 𝑔. What does this function represent?

MTH 111 College Algebra Exam 3, Part 2

Name ______________________

Student ID ______________________

3. The number of oranges grown by a tree depends on how densely the trees are planted at a farm. If 𝑛 trees are planted on an acre of land, then each tree produces 630 − 9𝑛 oranges. Thus, the number of oranges produced per acre is 𝑂(𝑛) = 𝑛(630 − 9𝑛). How many trees should be planted per acre to get the largest yield of oranges?

4. Find a polynomial of degree 5, with zeros -1, 0 (multiplicity 2), 1, and 2, and that has a coefficient of 𝑥 of 4.

5. For the function 𝑟(𝑥) = , find all holes, intercepts, and asymptotes, sketch

the graph, and state the domain and range.