New ReviewIn this video we are going over the beginning of how to graph a logarithmic function. This is the video you will want to watch first before going deeper.

New ReviewIn this video we are going to explore how to find the vertical, horizontal and slant asymptotes of Rational Functions as well as the x and y intercepts

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 ReviewIn this video, I compare graphing an "easy" logarithmic function with a "harder" one, detailing the steps for both. We focus on how to graph logarithms, including their transformations and asymptotes, which is crucial for understanding...

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

New ReviewIn this video, I provide five tips for graphing logarithmic functions, especially if you struggle with graphing logarithms. We'll cover how to graph logs and address common mistakes, including understanding asymptotes to accurately plot...

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

New ReviewIn this video, I'll walk you through how to graph cosecant functions, especially when they include a phase shift. We'll cover the amplitude and period to accurately graph the cosecant graph by first understanding its related sine...

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...

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 we are going to explore how to find the vertical asymptotes and holes of a rational function. We will look at three different functions to help us identify if it is a hole or asymptote

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

In this video we will explore how to graph a logarithmic function from starting with an easy function and then working our way to a more advanced difficult function.



✅ Simple Tip to Solving Exponential Equations -...

Why imaginary numbers are needed to understand the radius of convergence

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...