Category Archives: College Algebra

Find a Function with Asymptotes

Posted on October 14, 2009 by eric

In this pencast I find a function that satisfies a particular condition — the function should have a vertical asymptote at x=1 and a horizontal asymptote at y=2. find func w assymtsbrought to you by Livescribe

Posted in Pencast, Plotting, Graphs | Tagged , | 3 Comments

Find Extrema and Classify Function

Posted on October 14, 2009 by eric

In this problem, I use derivatives to find the local maximums and minimums of a function and determine the intervals on which the function is concave up or concave down. find extrema classifybrought to you by Livescribe

Posted in Pencast, Plotting, Graphs | Tagged , , | 3 Comments

Finding Inflection Points

Posted on October 14, 2009 by eric

Trigonometric functions have plenty of inflection points, local maximums and local minimums. Why? Because they’re periodic — they repeat. Selecting a particular interval gives you the opportunity to find a limited number of inflection points. inflection pts over intbrought to … Continue reading →

Posted in Pencast, Trigonometry | Tagged , | 1 Comment

Cylinder Linear Approximation

Posted on October 9, 2009 by eric

Linear approximations aren’t very intuitive when you’re only looking at symbols on a page. In this problem, I make it easier to understand how and why linear approximations are useful, and make it easier to digest by using a physical … Continue reading →

Posted in Linear Functions, Pencast | Tagged , | 2 Comments

Linear Approximation

Posted on October 9, 2009 by eric

A function’s graph may have maximums, minimums, spikes and strange looking things. These characteristics can make it difficult to calculate the derivative of the function. Here’s where linear approximation can come to the rescue: Functions can be approximated by simple … Continue reading →

Posted in Linear Equations, Pencast | Tagged , , | 5 Comments

Evaluate the Limit of a Function… as it Approaches Infinity

Posted on September 26, 2009 by eric

In a previous pencast, I evaluate the limit of a function as it approaches a particular point. But what about evaluating the limit of a function as you move along the x-axis toward infinity? Holes exist as points on a … Continue reading →

Posted in Factoring, Roots, Pencast, Plotting, Graphs | Tagged , , , , , | 3 Comments

Absolute Value Functions, Holes, and Limits

Posted on September 26, 2009 by eric

With absolute value functions, it’s always important to keep in mind what domains apply to your function. With this equation we’re presented with the pesky problem of dividing by zero, and the consequences of having holes in the graph. Don’t … Continue reading →

Posted in Function Operations, Pencast, Plotting, Graphs | Tagged , , | 4 Comments

Evaluating the Limit of a Rational Function, at a Point

Posted on September 26, 2009 by eric

Always remember that you can’t divide by zero. Up until now, stumbling upon a situation where you divide by zero leaves you with a mysterious problem that you don’t know how to solve. However, if you understand what limits are, … Continue reading →

Posted in Pencast, Plotting, Graphs | Tagged , , , | 2 Comments

Graphing a Function with Holes

Posted on September 26, 2009 by eric

Some functions are full of holes when you graph them. What are holes, you might ask? Well, they’re not the kind that will cause a leak. Knowing what holes are, and how they relate to limits can be problematic, but … Continue reading →

Posted in Logarithms and Exponentials, Pencast, Plotting, Graphs | Tagged , , , | 4 Comments

Evaluate the One-Sided Limit of a Function

Posted on September 25, 2009 by eric

Always remember that you need to keep track of the conditions that make the denominator of an algebraic expression equal to zero. Even though you can’t evaluate an expression when you’re dividing by zero, you can however calculate an expression … Continue reading →

Posted in Function Operations, Pencast, Plotting, Graphs, Polynomial Algebra | Tagged , , , , | 2 Comments

Finding Piecewise-Function Limits

Posted on September 25, 2009 by eric

Piecewise functions are singles collections of sub-functions (each one constituting a “piece”, hence “piecewise”… and why you can think of them as “sub” functions), defined for specific parts of the domain of a graph. When we look at piecewise functions … Continue reading →

Posted in Pencast, Plotting, Graphs | Tagged , , , , | 3 Comments

Exponents… The Rules

Posted on September 22, 2009 by eric

In this pencast I discuss some of the fundamentals rules you need to know when you’re dealing with exponents. This is important because it provides a good sequeway into more advanced topics, like the log function (they’re great to build … Continue reading →

Posted in Logarithms and Exponentials, Pencast | Tagged , , | 2 Comments

Solving Equations That Include Logarithms

Posted on September 22, 2009 by eric

What’s the point in learning about the rules that involve logarithms and exponential functions? To solve equations that we’ve never seen before. Have your quadratic formula handy for this one (if you haven’t already memorized it…), as well as a … Continue reading →

Posted in Function Operations, Logarithms and Exponentials, Pencast | Tagged , , | Leave a comment

Simplifying an Exponential Function

Posted on September 22, 2009 by eric

Now that you understand the basic properties of logarithms and exponential functions, it’s time to put your knowledge to use. Remember that the natural log and e^x functions are the inverse of each other. Also — simplify things whenever, and … Continue reading →

Posted in Logarithms and Exponentials, Pencast | Tagged , , | 1 Comment

All About Logs

Posted on September 20, 2009 by eric

Here, an expression with logarithms is simplified. It’s good to watch the pencast “exponents… the rules” for background information. all about logsbrought to you by Livescribe

Posted in Logarithms and Exponentials, Pencast | Tagged , | 1 Comment