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Precalculus – Fall 2020

Name

Exam 2 – (50 points)

Directions: Work each problem on your own paper showing sufficient work to justify your solutions. You

must make progress toward a correct solution in order to receive partial credit. Upload your work to Moodle when

you are finished.

1. (6 points) Find the solution to the inequality. Write your answer in interval notation.

(x − 5)(2 − x)

≥0

(x + 3)2 (x + 1)

2. (6 points) Find the domain for f (x) =

p

x2 − 2x − 8. Write your answer in interval notation.

3. (6 points) Give the equation of the function shown in the graph below.

4. (6 points) Provide a rough sketch of the curve y = (x − 2)3 (x + 1)2 (x − 3)2 (1 − x). Make sure all roots are

identified, the graph is positive and negative in the correct intervals, and the curve has the correct general

shape.

5. (8 points) Consider the function g(x) =

• What are the roots?

(x + 1)2 (1 − x)

. Answer the questions below and sketch the graph.

(x + 3)(x − 2)2

y

6

• What are the vertical asymptotes?

-x

• Are there any holes? If so, where?

• Is there a horizontal asymptote? If so, where?

6. (6 points) Give the equation of the rational function plotted below.

7. (6 points) A workshop makes small crafts. If they make x per day, they can sell each of them for a price, in

dollars, given by p = 200 − 4x. Determine the number they should make to maximize their revenue.

8. (6 points) A farmer wishes to enclose a rectangular area divided into two sections as shown in the figure below.

One side of the region will be an existing wall. The rest will be constructed using 1500 feet of fencing. What

dimensions will enclose the maximum possible area?

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Tags:

vertical asymptotes

rational function

interval notation

horizontal asymptotes

original inequality

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