Professor Lewinson- Transformations

Hello class my name is Professor Lewinson and today I am going to teach you about the incredible world of transformations. After the lesson is over feel free to contact me addressing any issues you are still facing with this particular topic. Now lets start with the basics...

What is a transformation?

A transformation is an operation that moves the points of a figure in a plane.

But wait there's more! Some types of transformations include reflections, shifts, stretches and compressions. We are able to see transformations when we look at two or more graphs side by side. The figure starts in one place and suddenly its stretched, shrinked, flipped over, or pushed way to one side! Using what we are about to learn will help us understand why each of those things happen.

Today we will be focusing on shifts. So here is your original graph: (for the purpose of this lesson [ ] will be used as our absolute value signs simply because I'm bad with technology and cannot find where the real absolute value sign is :) )

f(x)= [x]   which when represented on a graph would look like this



Now say we have a number inside the absolute value with the x, this will shift the graph from side to side. f(x)= [x+1] will send the graph over one space to the left and f(x)=[x-1] will send the graph over one space to the right. I think the easiest way to remember it is that when a number is on the inside is goes the opposite way that the sign is telling you. So if you have a negative sign in front of the number you are going towards the positive side of the x axis and if it is a positive sign you go towards the negative side of the x axis.

Now we look at what is outside of the absolute value. (This one is much simpler if the number outside is negative the figure shifts down and if its positive it goes up!) for example: f(x)= [x] +1 you guessed it! It is going to shift the entire graph up one unit. Now say we have f(x)= [x] -1 the whole graph shifts down.

For the last few minutes of our lesson I want to talk about how this might be used in a real life example. Say we have a table that we don't like downstairs and we want to get it upstairs. If we were to figure it out mathematically we would need to find the number of feet we need to go sideways and the number of feet we need to go when we go up the stairs. For shifts, nothing is happening to figure it is simply being moved to another location.

Tomorrow we will be building off of this base transformation knowledge and learning about stretches and compressions. Hope you enjoyed the lesson!