New ReviewIn this video we are going work on graphing a rational expression with 4 vertical asymptotes.

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 ReviewIn this video we are going to explore how to identify the foci and asymptotes of a hyperbola

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 ReviewNot all problems should be done in your head, but sometimes it is advised to do math in your head. Here are my top problems I want my students to be able to do.

New ReviewIn this video, I'll walk you through graphing cosecant functions by first focusing on the reciprocal sine graph. We'll explore the process for y=csc(2x) by understanding its relationship to y=sin(2x), covering key elements like amplitude...

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

Today we explore the intriguing concept of time constants in LR circuits. Building on our previous derivations, we unravel the significance of the time constant, expertly explained by Bobby. The time constant, represented as the ratio of...

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

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 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...

👉 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 solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a...

👉 We will explore how to evaluate the limit at infinity. When evaluating the limit at infinity or negative infinity we are interested to know where is the graph going right and left. This is also commonly explored as end behavior of the...

👉 Learn how to evaluate the limit of a function involving trigonometric 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....

In this lesson, students learn how to identify holes in a graph by investigating functions. They explore examples where the denominator of a function cannot equal zero, resulting in either an asymptote or a hole in the graph.

👉 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...

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a...