# Syllabus

**Functions**

3.2.1 determine when the composition of two functions is defined

3.2.2 determine the composition of two functions

3.2.3 determine if a function is one-to-one

3.2.4 find the inverse function of a one-to-one function

3.2.5 examine the reflection property of the graphs of a function and its inverse

**Sketching graphs**

3.2.6 use and apply |*x*| for the absolute value of the real number x and the graph of *y* = |*x*|

3.2.7 examine the relationship between the graph of *y*= *f*(*x*) and the graphs of , *y*= |*f*(*x*)| and *y*= *f*(|*x*|)

3.2.8 sketch the graphs of simple rational functions where the numerator and denominator are polynomials of low degree

# Lessons

## 1. Functions and their inverses

Note that the graphs in this Prezi are animated. Click on the play button to run the animation.

The wikipedia page on Set-builder notation is worth looking at for further details of how to specify domain and range.

## 2. Composite functions

## 3. Absolute values and functions

Graphs of absolute value functions in the general form

(click on the picture for an interactive version of the absolute value graph)

## 4. Graphs of (y=f(x)) and (y=frac1{f(x)})

## 5. Rational Functions

## More about absolute value functions

It’s difficult to know just how much to include about absolute value functions. The information below is old content that *may* be inferred to be included by the broad curriculum descriptions.

### Absolute value and inequalities:

To solve inequalities involving absolute values we make use of the relation (|a|leq b iff -bleq aleq b). For example: