MATH 411
Chapter 5
0.1
Definition 1: Lipschitz Condition
A function f (t, y) is said to satisfy a Lipschitz condition in the variable y on a set D R2 if a constant L > 0 exists with |f (t, y1 ) - f (t, y2 )| L|y1 - y2 | whenever (t, y1 ), (t, y2 ) D. The
Function Fact Sheet
Name of Function Family:_Linear_
Formula
The general formula for this type
of function (if there is one):
If there is not a general formula for this type of function, how do you tell if a given formula is
this type of function?
y = mx
1. y = log2(x+1)
2. A logarithmic function always has a vertical asymptote. The domain tells us this because
it never reaches one point, but always gets closer
3. They never have horizontal asymptotes. The range confirms this because it is evergrowing.
4.
Function Compare/Contrast Assignment
I. Complete the following chart by filling in each cell with an example and a description of how to
recognize each function when given in that representation.
Linear
Symbolic
y = mx + b
The highest power
on the variabl
Quadratic
Cubic
Example equation:
y
Rational
Example equation:
y
Example Data:
Example Data:
Example Application:
Example equation:
p ( x)
y
q( x)
Example Data:
Example Application:
Independent variable is
squared.
Graph is a parabola
To graph: find the
v
Day 9: Review for Unit 1 Test
Instructions:
Add instructions.
Answer the following six questions. For each statement below identify
whether it is true or false.
1. True or false? A relation is also a function.
2. True or false? The domain for (x)=2x2-3x+5
At the bottom of this file you will find the tabs for each of the nine function families that we will learn about in Unit 1.
To explore, choose the family that you want to learn about by clicking on the appropriate tab.
As you change the numbers in the gr
Transformations
Practice Identifying
This PowerPoint allows you to practice what you know about
transformations. Get a piece of paper (and maybe even some graph
paper). Write down your answers to each question. Only then
should you go on to the next slide
Solving the Simplest
1. Solve each of these matrix equations by first turning them into a system of linear
equations by using the multiplication algorithm that we developed in class (please
read the reference: Matrices and Linear Systems) and then using o
1. y = x
2. This would look like this:
3. y =
3 x
4. This would look like an S like this:
5. Radical functions never have an end, a maximum, and are never not one-to-one,
6. When you swing back and forth on a swing at the park, how long it takes you to co
My two equations were the standard equation of y=0.25x2-3x+10.5 and the transformation
equation of y=0.25(x-6)2+1.5. To convert from the standard, you would do this:
y=0.25x2-3x+10.5
y=.25(x2-12x)+10.5
y=.25(x2-12x+36-36)+10.5
y=.25(x-6)2-36)+10.5
y=.25(x