Curated Video
Determining End Behavior of Graphs by Analyzing Equations
In this video, the teacher explains how to determine the end behavior of a graph by analyzing its equation. They discuss power functions with even and odd exponents, and how the graphs change as the exponent increases. The teacher also...
Brian McLogan
Adding two functions and finding the domain rational and radical
👉 Learn how to add or subtract two functions. Given two functions, say f(x) and g(x), to add (f+g)(x) or f(x) + g(x) or to subtract (f - g)(x) or f(x) - g(x) the two functions we use the method of adding/subtracting algebraic expressions...
Catalyst University
Lineweaver-Burke Plots Introduction and Theory
Lineweaver-Burke Plots Introduction and Theory
Curated Video
Comparing Polynomial and Exponential Growth: Tables and Graphs
In this lesson, we observe that as X approaches infinity, both polynomial and exponential functions approach infinity. However, through examples and graphs, we discover that exponential functions eventually surpass polynomial functions...
Professor Dave Explains
Logarithms Part 2: Base Ten Logs, Natural Logs, and the Change-Of-Base Property
An introduction to logarithms.
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 find increasing decreasing intervals and extrema of a function
👉 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
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...
Catalyst University
Series | Limit Comparison Test: Example 2
Series | Limit Comparison Test: Example 2
Brian McLogan
Learn how to determine concavity of a polynomial function
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down. To test for...
Curated Video
Determining the Equation of a Polynomial Graph
In this video, the teacher explains how to determine the equation of a polynomial graph by analyzing its end behavior and zeros. They provide examples and step-by-step instructions, highlighting the importance of understanding...
Math Fortress
Differential Equations: Families of Solutions (Level 4 of 4)
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over an example illustrating how to verify a particular solution of the one-parameter family of solutions,...
Brian McLogan
Use baby numbers to evaluate the right hand limit 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
How to find the vertex and axis of symmetry then graph using a table of values
👉 Learn how to graph quadratics in standard form. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a...
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
Determine the left and right hand limits using infinity of a 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...
Catalyst University
Power Series: Computing Integrals via Power Series: Example 1
Power Series: Computing Integrals via Power Series: Example 1
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...
Catalyst University
Power Series | Power Series & Interval of Convergence: Example 3
Power Series | Power Series & Interval of Convergence: Example 3
Professor Dave Explains
Particle in a Box Part 1: Solving the Schrödinger Equation
Now that we understand the Schrödinger equation, it's time to put it to good use, and solve a quantum problem. Let's find the eigenfunctions and eigenenergies associated with a quantum particle restricted to an infinite square well. This...
Catalyst University
Series | Alternating Series Test (with Conditional/Absolute Convergence): Examples 1 & 2
Series | Alternating Series Test (with Conditional/Absolute Convergence): Examples 1 & 2
Brian McLogan
Domain of a rational function by factoring
👉 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
Overview of implied domain of functions
👉 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...