Polynomial and Rational Functions Review

This tutorial provides a comprehensive review of polynomial and rational functions, focusing on solving multiple choice questions, determining polynomial degrees, graphing rational functions, solving algebraic equations, and understanding graph behavior near asymptotes. It includes detailed explanations and examples to enhance understanding of these mathematical concepts.

What is the main focus of this tutorial?

• Exploring advanced calculus techniques

• Detailing solutions to polynomial and rational functions test review

• Discussing geometry and trigonometry

• Reviewing basic algebra concepts

For a cubic function, which row of differences is consistent?

• Fourth row

• Third row

• Second row

• First row

What characteristic defines an even function?

• f(x) = 0

• f(x) = -f(x)

• f(x) = x

• f(x) = f(-x)

Which transformation involves a reflection in the x-axis?

• Vertical translation

• Reflection in the x-axis

• Horizontal stretch

• Vertical stretch

What is the domain of a function with factors in the denominator?

• All real numbers

• All integers

• All real numbers except where the denominator is zero

• All positive numbers

How do you determine the degree of a polynomial from a table of values?

• By counting the number of terms

• By checking the constant term

• By finding the row where differences are consistent

• By looking at the highest coefficient

What is the general form of a quadratic equation?

• y = ax^3 + bx^2 + cx + d

• y = ax^2 + bx + c

• y = ax + b

• y = ax^4 + bx^3 + cx^2 + dx + e

What is the horizontal asymptote of a rational function where the degrees of the numerator and denominator are the same?

• The ratio of the leading coefficients

• Undefined

• Infinity

• Zero

How can you determine if a rational function crosses its horizontal asymptote?

• By checking the y-intercept

• By setting the function equal to the asymptote and solving

• By looking at the graph

• By finding the x-intercept

What is the solution to the equation x + 3/8 = 2x?

• x = 5/8

• x = 1/5

• x = 2/3

• x = 3/5