Exam 3: Polynomial and Rational Functions

Suppose a species of sea turtles is confined to an island and has a current population of 75 turtles. If the population, N, is modeled by where t is the time in years, how many turtles are predicted to be on the island in 22 years? Round to the nearest integer.

Find all zeros of the function .

Consider the function . Find the function's domain and identify any horizontal and vertical asymptotes.

Find all real zeros of the polynomial and determine the mutiplicity of each.

Using a graphing utility, graph and approximate the zeros and their multiplicity.

Write the complex conjugate of the complex number .

Using a graphing utility, graph and approximate the zeros and their multiplicity.

If , use synthetic division to evaluate .

Use long division to divide.

Use the quadratic formula to solve .

Simplify the rational expression, , by using long division or synthetic division.

Write the quadratic function, , in standard form.

For the function given below, determine the domain, the x-intercepts, and any vertical and horizontal asymptotes. Use all of this information plus any additional solution points as needed to sketch the graph of the function.

Find the zeros (if any) of the rational function .

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is .

Consider the function . Identify any slant asymptotes.

Find all the real zeros of .

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Simplify the rational expression, , by using long division or synthetic division.

Write in the form when .