Math 107 test

Math 107 Assignment #4 - Summer 2020

-Chapter 5-

Due on Sunday May 31st

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 polynomial function f(x) = −2(x + 2)2(x − 7)3.

(a) List each real zero and its multiplicity

(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.

(c) Determine the end behaviour of the function by using the leading term.

(d) Using parts (a)-(c) create a rough graph of the function that illustrates the intercepts, the crossing or touching of them on the x-axis, and the end behaviour.

2. Graph the rational function R(x) = x2 + 4

x2 − 1 using the seven step procedure for graphing

rational functions. Reminder to show your work for each step.

3. Solve each of the inequalities below.

(a) (x − 1)(x + 3)2 > 0

(b) (x + 5)2

x2 − 4 ≥ 0.

4. Use the Rational Zeroes Theorem to factor and solve x4 + x3 − 3x2 − x + 2 = 0.