Piecewise Functions

Thanks to Alex Beltechi for this tutorial on PSD Tuts.

This is the first graphic that I needed Adobe Illustrator to complete.  Also, it was the first that took me multiple sessions to complete.  I really like the effect for piecewise functions though.  I always teach this topic by describing piecewise functions as a combination of different parts of multiple functions.  We start by graphing each individual rule and highlighting the parts of each that will be used for the new function (as specified by the domain).  This illustration gives a good starting point for the discussion as each letter is a piece of the complete word.  Something of a simple idea, but that's definitely where we want to start with piecewise functions.

Power Rule

Thanks to Arik for this tutorial on PSD Tuts.

I really liked the look of this text effect when looking through tutorials so I used it for the Power Rule.  The power rule is usually the first lesson in Calculus, after limits and the definition of derivative, where students really start to see the beauty and ease of the subject.  It's an exciting lesson indeed!

Function Transformations

Tutorial posted by Unknown here on PS hero.

This was probably the first tutorial assisted graphic I created and it pretty much speaks for itself.  If I was to change anything, I'd add the Autobot and Decepticon icons somewhere and may do that in the future.  Transformations are now found throughout the Tennessee high school math standards so I can use this graphic over and over.  Though it's not a full page graphic, just put it on a black background and it blends perfectly.

12 Basic Functions

Background image used from this tutorial on ps deluxe.

Precalculus: Graphical, Numerical, Algebraic (Demana, Waits, et al.), probably the most popular high school precalculus textbook, contains a section titled "12 basic functions".  I think the lesson provides a great overview of function theory and leaves plenty of room for discussion.  When teaching the lesson, I have students make a small flip book with the graphs of the parent functions on one side and the name and facts on the other.  Later, I let them use these books when we study transformations.

Above I've included an animated gif on top and a simple graphic on bottom.  I've been really surprised that adding the slightest bit of animation to Smart board presentations makes a huge difference in captivating the class.  I based the graphic (loosely) on this recent graphic created for the Dave Matthews band.

Conic Sections

Thanks to Rose for this tutorial on PSD Tuts.

I don't know about you, but Conic Sections was always one of those lessons that I seem to either barely touch on at the end of Precalculus, or just end up skipping altogether.  It's not that I don't like the lesson but the amount of material that is covered can be staggering, taking up precious time that can be used for other concepts needed in Calculus.  Thankfully, Tennessee state standards for Algebra 2 have included Conic Sections heavily in their newest version.  Also, the ACT has included these concepts more and more over the past 10 years. 

While introducing the different conic sections we always start with the familiar ones: lines, parabolas, and circles.  Usually around the time we start talking about conic sections and quadratic regressions the MLB (Major League Baseball) is in the climax of the season.  So, one of the applications I mention is measuring the distance of a home run.  Most of the students know that home runs are measured and compared, but they never really think about the fact that the measurement is given right when the home run occurs.  No one is out there with a tape measure or yard stick.  It's a great discussion to introduce parabolas, quadratic regressions, and the many applications of conic sections.