Overview
1. Consider a fifth-degree polynomial function with the following properties:
a).It has zeros of multiplicity one at r = -2, -4,6 and a zero of
multiplicity two at x = 3.
b).It has end behavior like that of the equation y = -x^5
Sketch a graph for a function with these properties.
2.Let f(x) = 3x^4- 5x^3 - 13x^2 + × +6
a)Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros of f(x).
B)Use the Rational Zeros Theorem to write a list of all possible rational zeros of f(x).
C)List all the zeros of f(x).
D)Write f(x) in factored form.
3. Describe any horizontal or vertical shifts and reflections for the following equation, compared to y =\sqrt{x}
Y=\sqrt{-x-5}+4
4. Find the complex solutions of the following equation. Simplify your solutions into a+bi form.
3x^2+6x+4=0
5. Find the domain of the following function. Express your answer in interval notation. g(x)=\frac{\sqrt{x+3}}{x-2
7. Find the equation of the line with the given properties. Leave your answer in the Slope-Intercept Form:
Passes through (4, -1) and is perpendicular to the line 3x - 5y = 1