Transformations

Hello all, this is Lina with today's scribe post.

This morning we went over the last question on our pre-test from yesterday. Miller has the answers to the questions from the pre-test in his post yesterday. We also had a practice question where we had to draw out a graph and write a second equation for it. That can be seen in the first slide post for today. In the first post of "Today's Slides" are questions to help us review for the test tomorrow during fourth period. Don't forget to do them! We were also asked to complete Exercise 7.

After all that jazz, we went on to start our new unit, "TRANSFORMATIONS". How exciting.
A simple definition of would be that: transformations are operations that change or alter the way that a function looks.
The type of transformation that we've learned today was Translation. A definition of a translation would be that it changes the position of the function without modifying its size or orientation. Basically it would shift the function to a different point on the graph.
The general equation for this would be ----> y= f(x - a) + b
In the equation, a would move the function left or right where b would move the function up or down.

For example, we were given this question in class today:
The graph of g(x) is formed by sliding f(x) 4 units to the left. If f(x) = sin(x-2) + 5, write the equation in terms of sine to represent g(x).


The graph for f(x) would look like this:



Now, the graph for g(x) is moving 4 units to the left. We know the general equation is y= f(x-a)+ b and we know it's a that has to change because it's the one that moves the function left or right.

If f(x)= sin(x-2)+5. Then g(x)= sin(x+2) + 5 so that the function shifts 4 units to the right as shown in green in this next graph.

You can count it if you like, but I assure you it has shifted 4 units.

Using the same equation of : f(x)=sin(x-2)+5, we can also shift the function up or down by changing the b value. If we wanted to say, find g(x) by shifting the f(x) down by 3 units, the equation would look like: g(x)=sin(x-2)+2. f(x) is shown in blue, g(x) is shown in green.

Pretty easy right? So let's conclude. Translation is when we shift the function to a different point on the graph without changing its size or orientation. The general equation for the function is: y=(x-a)+b. While using translation, the only values we would change would be the a and b values.

With that said, I will now end my post. I hope I did our new unit justice and I hope you all understand what I was trying to explain.

REMEMBER! Our test is tomorrow, fourth period! So study, study!

Last, but not least, the next scribe will be... GOAT.