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
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
Applying the first derivative test to a polynomial to determine the increasing and decreasing
👉 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...
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
Solve a quadratic using the quadratic formula with complex answers
👉 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...
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
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
Determining if a function is a polynomial or not then determine degree and LC
👉 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...
Brian McLogan
Completing the square to identify the foci center and vertices of an ellipse
Learn how to graph horizontal ellipse which equation is in general form. A horizontal ellipse is an ellipse which major axis is horizontal. When the equation of an ellipse is written in the general form, we first rewrite it in standard...
Brian McLogan
Learn to determine the points where a function is non differentiable
👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative exists at each point in its domain. To check the differentiability of a function, we first check that the function is...
Brian McLogan
Finding the Slant Asymptote
👉 Learn how to find the slant/oblique asymptotes of a function. A slant (oblique) asymptote usually occurs when the degree of the polynomial in the numerator is higher than the degree of the polynomial in the denominator. To find the...
Brian McLogan
Learning to write the domain of a rational function with an asymptotes and hole
👉 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
Explaining if the tangent function is a continuous function or not
👉 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...
Brian McLogan
Learn to determine the value that makes the piecewise function continuous
👉 Learn how to find the value that makes a function continuos. A function is said to be continous if two conditions are met. They are: the limit of the function exist and that the value of the function at the point of continuity is...
Brian McLogan
Learn how to identify if a function is a polynomial and identify the degree and LC
👉 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...
Brian McLogan
Determine the values a function is undefined and write the domain
👉 Learn how to find the domain of rational functions with radicals in both the numerator and the denominator. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function,...
Curated Video
Graphs of Trigonometric Functions
In this lesson, students will learn about the graphs of the four trigonometric functions (tangent, cotangent, secant, and cosecant) by relating them to the sine and cosine graphs. They will understand the patterns, zeros, and asymptotes...