MATH115 Pre-Calculus

Quiz 1

Instructions: The quiz is worth 30 points. There are 6 problems. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). Show work/explanation where indicated. Answers without any work may earn little, if any, credit.

1. Solve the following equation:

2. Solve the following inequality. Express your answer in interval notation.?

3. Do the points A(1, 2), B(6, 0) and C(3, 6) form a right triangle? Justify your answer!

4. A farmer uses 300 feet of fencing to make a rectangular pen. The farmer will need fencing on only 3 sides because a straight river will serve as one side of the pen (instead of fencing). The area of the pen can be described by the following function: where x is the length of each of the two sides of pen perpendicular to the river. Find and interpret (with a picture) each of the following: A(60), A(80) and A(100).

5. Graph the function from problem 4 and find the value of x that makes the area of the pen a maximum.

Graph (hand made):

6. Given the graph of y = f(x) below (on the left). Use transformational techniques to graph (on the right) y = 5 – f(x + 2).