Introduction to Basic Transformations: Translations of Functions

Hello everyone! For those of you who don't know me, my name is Marynea Collina (or just Nea; however, I have been trying to convince everyone to call me using my full name because it sounds ambiguous.) I am the one sitting at the front who is either talking uncontrollably or on the verge of falling asleep. (Just kidding.)

But enough about me! Anyway, I am here to "attempt" to summarize what we've learned today. "Attempt" because I was doing the latter during Pre-Cal. Close to falling asleep, that is. (Just kidding. Don't hate me, Mr. P. The class is cool. Really. I promise. It really is.) In case you guys weren't paying attention, it was about Genetics. Well, in case you aren't paying attention again, I was only kidding. Today, what we REALLY talked about was the Translations of Functions, which marks the first lesson of the second unit.

Mr. Piatek introduced the unit with a recap of the lessons we covered back in Grade 11 (which I hope you remember still): functions, quadratics, graphing. As we all know, function is a relation which assigns exactly ONE element in this range for each element in its domain.

Just for the purpose of making myself and everyone else remember, here's a quick recap of it:
                            f(x) = y ---> it means that for every x value, there is only one y value.

One easy way to know if it's a function or not is to make a table of values. Another is to do a vertical line test. If it intersects the graph twice, then obviously it is not a function. Therefore, a circle cannot be a function.

y = x^2

The graph on the left side shows a parabola that can be considered a function; the lines should only intersect once.

You can also create a table of values:

• x	y
  -2 -1  0  1  2	4 1 0 1 4

You will be able to see that there's only one X for everything. There might be y-duplicates, but Xs continued to be unique (if that makes sense).



I won't explain any further because I know you guys know about it already. If you need help, just ask Mr. P anytime, or even me. (Do the latter if you want to fail.)

Now that you remember how to graph functions or what they really are at all, we are now able to shift the graph of functions.

He introduced a new topic (perhaps not so new to some people) which was Transformations. It is the moving, flipping, stretching, or compressing of the base graphs. It could either be: translation, reflection, or stretch. Unfortunately, we only got to Translations, which are the horizontal and vertical movements (shifts) using basic shape.

A few rules that it contains are:

1. Vertical Translations:  only y values are affected
    y = f(x) + k ------> shifts the entire graph up k units
   y = f(x) - k --------> shifts the entire graph down k units
2. Horizontal Translations: only x values are affected
   y = f(x-h) ---------> shifts the entire graph right h units
   y = f(x+h) --------> shifts the entire graph left h units

Remember! k values remains as is and h values must be read as opposite.
      example: f (x-4): h = +4

Here's an example from the booklet that we solved in class:

For b), it indicates a vertical translation, therefore not affecting the y-values, only x. f(x) + 3 asks for the x-values to be shifted upwards by 3 units (since it's positive 3 and a k-value, it ought to stay as is). So you add 3 values to the x-values:

0+3 = 3
1+3 = 4 ... etc.

Although for c), it is a horizontal translation, so x values change. f(x-3) contains an h-value, so we read it as an opposite value. -3 ---> add 3 units for y-value (to the right).

0+3 = 3
1+3 = 4
4+3 = 7 .. etc.

Oh well, I don't think I have anything else to say. It was the beginning of the unit and didn't really contain that much substance. Although, I bet this topic will play a big part for the remaining of this course. I'm half-asleep right now. Always will be. I hope I made any sense. If you seriously need any help still, don't be afraid to ask Mr. P or your peers. I am here to support as well! Don't forget to do your homework. xx

Yours Truly,
Marynea Collina ヾ(＾∇＾)

(P.S: Is anybody reading this at all? Let's make a petition to make Mr. P to change the background of our blog. Seriously. Am I the only one who cares about the background?)