Curated Video
Zeros
A video entitled "Zeros" which shows how to find key features of a rational function in order to graph it.
Curated Video
Interpret Exponential Features
New ReviewA video entitled "Interpret Exponential Features" that covers the shapes of exponential curves with different base values.
Curated Video
Key features of an exponential graph
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.
Curated Video
Key features of a reciprocal graph
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...
Curated Video
Advanced problem solving with non-linear graphs
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...
Curated Video
Basics / Transformations to Rational Functions
In this video, we define rational functions and examine how to graph simple rational functions as transformations to the reciprocal function.
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...
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
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....