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
Graph without a Vertical Asymptote No Vertical Asymptote
In this video we will explore how to graph a rational function when we have no vertical asymptote
Curated Video
Interpret Features of Functions
This video will review how to interpret the different features of linear, quadratic, and exponential functions.
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...
Brian McLogan
How to evaluate the limit to infinity of a rational function
👉 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
Evaluate the limit to infinity with ha asymptote
👉 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
Graphing the reciprocal function with multiple transformations
👉 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...
Brian McLogan
Given rational function find the vertical asymptote and hole
👉 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...
Brian McLogan
How to find the left and right hand limit by not using a calculator
👉 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
Characteristics of functions
👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls...
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
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
Limits at infinity
👉 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...
Brian McLogan
Evaluate the limit of sinx over x
👉 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....
Curated Video
Graphing Shifted Exponential and Logarithmic Functions
In this lesson, students will learn how to graph shifted exponential and logarithmic functions by considering the spread of an Internet video. They will understand how changing the base affects the rate of growth or decay, and how...
Brian McLogan
Evaluate the left hand limit at an asymptote algebraically
👉 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...
Curated Video
Identifying Holes in Graphs: Investigating Functions
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.
Brian McLogan
Write the domain in interval notation of a 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...
Brian McLogan
Learn how to determine 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
Left hand Limit of a rational function at a hole
👉 Learn all about the Limit. In this playlist, we will explore how to evaluate the limit of an equation, piecewise function, table and graph. We will explore continuity as well as discontinuities such as holes, asymptotes and jumps and...