How the right question about Newton's method results in a Mandelbrot set.

New ReviewIn this video we are going to work on the common mistakes I see students make when trying to identify the x and y intercepts of a rational function

New ReviewWhen you need to graph a rational function there are a couple of things you must know.

New ReviewIn this video I am going to highlight the top ten types of functions that students make mistakes with when finding the domain and range

A video entitled "Zeros" which shows how to find key features of a rational function in order to graph it.

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.

In this video, we define rational expression, and find the domain of rational expressions.

In this video, we examine one situation in which rational functions could be used in the real world.

In this video, we define rational functions and examine how to graph simple rational functions as transformations to the reciprocal function.

In this video, we graph rational functions where the numerator has the same degree as the denominator.

Find all six trig ratios given a point on the terminal side of theta. In this video we work this common type of problem. We use the Pythagorean Theorem to find "r" (hypotenuse), and then use the given "x" (adjacent) and "y" (opposite) to...

What are some applications of rational functions? In this video we see a real-life example of rational functions and horizontal asymptotes.

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.

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 -...

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 -...

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...

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...

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...

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...

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...

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...

👉 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...

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...

👉 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...