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
1.
2.
3.
4.
Y = x3
Y = -x3
Y = x3+4x2
Cubic functions always have a vertex where the graph changes directions. This occurs in
the middle.
5. A cubic function is never not one-to-one. It never ends, an
Experiencing Exponents
In 1974 Richard M. Nixon resigned as president of the United States, Hank Aaron hit 715
home runs to break Babe Ruths record, and one gallon of milk cost $1.57. Since 1974
the a
1.
2.
3.
4.
5.
Y = 2x
Y = -2x
It never has a vertical asymptote; this is shown by the limitless domain.
It always has a horizontal asymptote. This is shown by the limited range.
Exponential functions
Day 8: Unit 1 Vocabulary Quiz
Instructions:
Please answer the following questions. On your first attempt, try to complete this quiz
without the use of notes, or reference materials. This will let you
Applying Exponents
1. I have $5000 dollars to invest at 3% compounded annually (The bank pays me interest at
the end of each year. That interest becomes part of my principle for the next year.)
a. How
The Composition of Functions
Youve seen in previous activities that you can combine functions using arithmetic
operations. You can also create new functions from old ones by first applying one
functio
Polynomial Characteristics
Use the Polynomial Factors app to investigate the characteristics of polynomials and
to answer the following questions (be sure to look at the various sheets or tabs at
the
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.
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 te
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 fo
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 r
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
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 t
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
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 variab
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.
Line
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
1.
List the Rule of Four for representing functions and give examples of each.
A formula, a graph, a real world example, and a table of numbers
Y=x,
6
4
2
0
, the amount you are paid compared to the h