Piecewise functions / Function Characteristics

We have dealt with piecewise functions somewhat when looking at absolute value functions.

Here are postal rates as a piecewise function:

Some of the piecewise functions in the text have semi-circles. The equation of a circle is x^2 + y^2 = r^2, where r is the radius. Circles can be translated like any other relation.

If you solve for 'y', you obtain the equation of the semi-circle (each of which is a function).

A better picture of each half of the circle from above.

Assignment from this sections is p70 #1-5.

Function characteristics are even, odd, increasing, decreasing, one-to-one, many-to-one.

Notes from this are located here.

Classifying Functions / Piecewise Functions

Period 4: Read through section 2.2 on classifying functions, then discuss the oral exercises on page 63 as a group.

Work on Q#1-4 on page 64 – specifically #3 – follow the instructions CAREFULLY!


Period 5: p70-71 #1-5 assigned.

Function Notation - Part 1

Most of Chapter 2 is review:

After the exam is done, discuss the Oral Exercises #1-15 on page 54 as a group – then work on p. 55 #1-10 individually.

Exam Day!

Unit 1 Exam - Period 4

Absolute Value as a Piecewise Function

Turning an absolute value equation into a piece-wise function:
Must do a sign analysis in order to decide where the negative applies:

How does the absolute value function affect the graph of a rational function - see the green line...