Sept. 20 Class

Learning Goals:

• Understand how to transform a single point.
• Review function notation.

Today I discussed another way to think about transformations by looking at individual points instead of the entire graph.

Example: If the point (1, 1) is on the parent function of , what point is the image of the point on the transformed function ?

We can use a chart to organize our response.

Across the top row are the transformations listed in order.  On the second row we consider whether the transformation would change the x or y value.  (HINT: horizontal transformations change the x value, vertical transformations change the y value.)

Solution: The image of the point (1,1) is (-2, 7).

We can use a chart like this to figure out what would happen to ANY point (x,y).  To see this we can add another row to the chart:

Thus, we can see that any point (x, y) changes according to,

This is called the transformation map.  If you map enough points, you can use this method to graph the final function.

Review

At this point it is good to being reviewing what we know so far to prepare you for the summative text on Tuesday!

First of all, you must know what a function is.

Function: a relation in which every x value is related to ONE y value.

You must be able to identify functions and non-functions.  Remember to use the vertical line test if you have a graph.

You must be able to understand and use function notation: y = f(x)

Give a function, you must be able to evaluate it for different values of x.

Example: Given f(x) = 3x + 2 and g(x) = 5x.  Evaluate 2f(3) + g(4).

Solution: 2f(3) + g(4) = 2[3(3)+2] + [5(4)]
                                   = 2[11] + 20
                                   = 42

Example: Given f(x) = 3x + 2 and g(x) = 5x.  Evaluate f(g(x)).

Solution: This means that you substitute g(x) into f(x).

f(g(x)) = f(5x)
           = 3(5x) + 2
           = 15x + 2

The previous example is what we call a composite function.  This could also be written as the following,

You should be able to recognize that f(g(x)) and f og(x) mean the same thing.

Homework: 
Complete worksheet on Composite Functions.
Pg. 70 #16-21