Sept. 7 Class

Learning Goals: Distinguish between linear and quadratic functions.

We began today by reviewing some of yesterday's homework.  Be sure you are clear on what a function is.

Then I discussed how to use set notation to write down the Domain and Range of a function.

If the function is given as a set of ordered pairs, we just need to list the values,

Example: What is the domain and range of the following function,

(2, 3)  (3,6)  (4, 8)  (5, 3)  (6, 3)

Solution: D = {2, 3, 4, 5, 6}  R = {3, 6, 8}

If we have a graph the domain and range is a bit more tricky.

Example: What is the domain and range of the following function?

Solution: The domain, x,  can be any value.  In set notation we write this as,

In words, we read this as "The domain is x in the real numbers".

The range, y, can only be positive.  In set notation we write this as,  

In words we say, "The range is y in the real numbers, such that y is greater than 0."

Next we talked about linear and quadratic functions.  These are two kinds of functions that we will be studying a lot of throughout the course.

If you are given a function as a table of values, you can tell if it is linear, quadratic or neither, by finding the first or second differences.

The first differences are the same, therefore this function is linear.

The second differences are the same, therefore this function is quadratic.

You can also tell by looking at the equation.  If the equation has degree 1, then it is linear.  if it has a degree of 2, it is quadratic.

Example: y = mx + b

This is linear because it has degree 1.

Example: y = ax² + bx + c

This equation is quadratic because of the x² it has a degree of 2.

For homework, please work on page 24, #1-9 (photocopied).