Section 2.2

Today we expanded a little on section 2.1 and began section 2.2.

The value of degree for a function is the maximum number of x-intercepts it can have.

First we touched up on some language and vocab that we would be using in the chapter.

• When referring to the highest possible point on a function, we use the word maximum. (Plural is maxima)

• When referring to the lowest possible point on a function, we use the word minimum. (Plural is minima)
• Both the maximum and minimum, when referring to both together, we use the term extreme points. (Plural extrema)

 As we looked at the value of degree in a function, we took note of some patters.

• The maximum degree of a function equals the maximum number of times that function can cross the x-intercept
• The maximum number of extrema (both maximas and minimas) equals one less than the highest degree of that function

 For example: If the highest degree of that function is 4, than the maximum number of extrema is 3. (4-1=3).

Than we looked at the end behavior of a function.

• If the x value increases and moves to the right, than   
• If the x value decreases and moves to the left, than
• If the y value increases and moves up, than 
• If the y value decreases and moves down, than

• If the maximum degree of the function is even, than the ends will move in the same direction
• If the maximum degree of the function is odd, than the ends will move in opposite directions

Than we talked about if were were given the zeros of a function, how we could find the function the were derived from.

Example: Zeros of the function are when x= -5, -1, 4

When x is -5 it means the (x+5)=0        When x is -1 it means that (x+1)=0
When x is 4 it means that (x-4)=0

So to write that as a function we just find the product of those three.
f(x)= (x+5)(x+4)(x+1) 
(And you can leave the equation like that for the most part, you won't be required to multiply it out)