3Blue1Brown
Where Newton meets Mandelbrot (Holomorphic dynamics)
How the right question about Newton's method results in a Mandelbrot set.
Curated Video
Zeros
A video entitled "Zeros" which shows how to find key features of a rational function in order to graph it.
Curated Video
Add and Subtract Rationals
A video entitled "Add and Subtract Rationals" which shows how to use a least common denominator to rewrite rational fractions so that they can be added or subtracted.
Curated Video
Domain of Rational Expressions
In this video, we define rational expression, and find the domain of rational expressions.
Curated Video
Basics / Transformations to Rational Functions
In this video, we define rational functions and examine how to graph simple rational functions as transformations to the reciprocal function.
Brian McLogan
My Five Step Method For Graphing a Rational Expression 5 Step Method
In this video I will go over my five step method for graphing a rational expression. We will work on the steps one by one.
Brian McLogan
Main things you need to know on finding the domain of a rational function
In this video I will explain the main points you need to know to understand how to find the domain of a rational expression. For each point I will apply some examples. ⭐ Find the domain of a rational function practice - • Find the domain...
Brian McLogan
What students always forget when writing the domain
Finding the domain or a function can be confusing, in this video I cover something students commonly forget when dealing with a rational radical function. ⭐️ Where Students Make Mistakes Evaluating Functions - • Where Students Make...
Why U
Algebra 94 - Rational Functions with Oblique or Curvilinear Asymptotes
In the previous lecture we saw that although a rational function may have any number of vertical asymptotes or no vertical asymptotes, rational functions will always have exactly one non-vertical asymptote. Unlike vertical asymptotes, a...
Why U
Algebra 93 - Rational Functions and Nonvertical Asymptotes
Although a rational function may have any number of vertical asymptotes or no vertical asymptotes, rational functions will always have exactly one non-vertical asymptote. Since a function's value is undefined at a vertical asymptote, its...
Why U
Algebra 92 - Rational Functions and Holes
In the previous lecture, we saw examples of x values that cause a rational function's numerator to be zero, where those x values produce x-axis intercepts in the function's graph. We also saw x values that cause denominator zeros that...
Why U
Algebra 91 - Rational Functions and Vertical Asymptotes
A rational function is any function that can be written as a fraction whose numerator and denominator are polynomials. Rational functions include a broad range of possibilities. For example, since a polynomial can be a constant, a...
Why U
Algebra 90 - Dividing Polynomials
This lecture explains a procedure used to divide polynomials that is analogous to the procedure used to divide integers called "long division". Dividing one polynomial (the dividend) by another (the divisor) produces a quotient that may...
Curated Video
Understanding a Simple Rational Function by Looking at a Graph and Table of Values
This video explains how to determine the relationship between two numbers when their product is constant. They use the example of paying for parking at a flat rate and demonstrate how the cost per person decreases as the number of people...
Brian McLogan
First derivative test relative extrema and increasing decreasing intervals
👉 Learn how to find the extreme values of a function using the first derivative test. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A method that can be...
Curated Video
Modeling Rational Functions by Graphing
In this lesson, mathematicians learn how to model rational functions by graphing. By using the example of sharing the cost of parking in a van, the concept of a rational function is explained. The graph shows how the amount of money each...
Brian McLogan
How to take derivative of a rational function using quotient rule
👉 Learn how to find the derivative of a function using the quotient rule. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the...
Brian McLogan
How to find the domain of a rational function - domain and range
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...
Brian McLogan
Learn how to write the domain of a rational function using interval notation
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...
Brian McLogan
Domain of a rational function by factoring
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...
Brian McLogan
How to find the domain of a rational equation
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...
Brian McLogan
Finding the implied domain of a function
👉 Learn how to find the domain of a radical function. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a radical square-root function, there cannot be a negative number inside the...
Brian McLogan
Evaluate the limit of a rational expression with a hole
👉 Learn how to evaluate the limit of a function involving rational expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The...
Brian McLogan
Learn to write the domain in interval notation of rational function
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...