New ReviewWhen trying to find the vertical asymptotes. Students will make a lot of mistakes. In this video we are going to explore some of the most common mistakes students make.

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

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

A video entitled "Interpret Exponential Features" that covers the shapes of exponential curves with different base values.

Pupil outcome: I can identify the key features of an exponential graph. Key learning points: - A exponential graph has a distinct shape. - An exponential graph has one asymptote. - The laws of indices explain where this asymptote is.

Pupil outcome: I can identify the key features of a reciprocal graph. Key learning points: - A reciprocal graph has a distinct shape. - A reciprocal graph has two asymptotes. - Reciprocal graphs of the form y = k/x have the axes as their...

Pupil outcome: I can use my knowledge of non-linear graphs to solve problems. Key learning points: - The shape of the graph can be used to identify the form of its equation. - Sketching the graph can help when solving problems. - Problem...

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.

In this video, we investigate how to 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...

In this video, we graph rational functions where the numerator and denominator have differing degree. We also do an example with a hole.

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 we will explore how to graph a rational function when we have no vertical asymptote

This video will review how to interpret the different features of linear, quadratic, and exponential 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...

👉 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...

👉 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...

👉 Learn how to graph the reciprocal function. A reciprocal function is a rational function whose expression of the variable is in the denominator. A reciprocal function is of the form f(x) = a / (x + h) + k, where h is the vertical...

👉 Learn how to find the removable and non-removable discontinuity of a function. A function is said to be discontinuous at a point when there is a gap in the graph of the function at that point. A discontinuity is said to be removable...