Exam 3: Polynomial and Rational Functions

Use polynomial division or synthetic division to rewrite the function, then sketch the graph using transformations of a parent function and the x- and y-intercepts (if they exist).

Use the Guidelines for Graphing Rational Functions to graph .

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation. x⁴ + 9 < 10x²

Use the following to answer questions : p(x) = x⁴ - 5x³ + 5x² + 5x - 6 -Apply Descartes's rule of signs to count the possible number of positive, negative, and complex roots (organize a table).

Give the location of the vertical asymptote(s) if they exist, and state the function's domain in set notation.

Graph the function. If there is a removable discontinuity, repair the break by redefining the function using an appropriate piecewise-defined function.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation. x² - 6x + 2 > 0

Determine the oblique asymptote, if it exists.

Use descriptive variables to write the variation equation for the statement. words typed varies directly as minutes spent typing

Use the following to answer questions : An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function , where P(x) is the profit in dollars and x is the number of automobiles made and sold. -How many cars should be made and sold to maximize profit?

Determine the location of the horizontal asymptote if it exists. Then determine whether the graph will cross the asymptote, and if so, where it crosses.

State the end behavior and y-intercept of the function. Do not graph. f(x) = -2x⁴ - 2x³ + x² - 2x + 5

Determine the location of the x- and y-intercepts (if they exist), and state the behavior of the function (bounce or cut) at each x-intercept.

Complete the square to write the function in shifted form. f(x) = x² + 6x + 1

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation.

Use the following to answer questions : (Gridlines are spaced one unit apart.) -Give the equation related to the graph. Assume |a| = 1.

Use the following to answer questions : (Gridlines are spaced one unit apart.) -State whether the degree of the function is even or odd.

Use synthetic division and the remainder theorem to show x = 1 - 3i is a zero of P(x) = -x³ - x² - 4x - 30.

Use the Guidelines for Graphing Rational Functions to graph .

Use the Guidelines for Graphing Rational Functions to graph .