Math 107 test

Math 107 Assignment #3 - Summer 2020

-Chapter 3 and 4-

Due on Sunday May 24th

Never leave your answer or work with decimals unless asked to. Show all work in order to receive full credit. Use a combination of English and Mathematical language to describe the solution to a problem where appropriate.

1. Consider the function f(x) = x

x3 − 4x .

(a) Compute f(1), f(3) and f(r + 2).

(b) Find the domain of f(x).

(c) Determine if f(x) is odd, even or neither.

2. Plot the graph of the piecewise function

f(x) =

  −3 x < −1 3x + 1 −1 ≤ x ≤ 1 5 x ≥ 1

Then state it’s range and any intercepts.

3. A wire 10 meters longs is to be cut into two pieces. One piece will be shaped as a square and the other piece will be shaped as an equilateral triangle. Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle. Then state the domain of this function.

4. By completing the square and applying a series of transforms on the function f(x) = x2 graph the function g(x) = −2x2 + 6x + 2. Then determine the maximum of this function.

5. Solve the inequality 6x2 < 6 + 5x.

6. A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway where fencing is not needed for the side that is shared with the highway. What is the largest area possible?