Section 3.3 Properties of Functions
This section will give you more tools to analyze functions.
A function f is increasing on an open interval I if, for any choice of x1 and x2 in I,
with x1 x2 , we have f x1 f x2 .
A function f is decreasing on an open i
Section 3.1: Functions
Before we begin our discussion of functions, lets talk about a relation. When
youve graphed lines before, such as y 2 x 3 , you graphed it by plotting x and y
values. That is because each x is related to its y-value by the rule y 2
Section 3.4 Library of Functions; Piecewise-defined Functions
Knowing
All the graphs we are going to go over you should memorize. You should know
what they look like without having to graph them out on paper.
1. Constant Function:
2. Identity Function:
3.
Knowing
Section 5.1 Polynomial Functions and Models
The word polynomial should be something you are very familiar with. In order to
be a polynomial function it must have only nonnegative integer exponents. This
means no negatives and no fractions as expon
Section 4.2 Linear Functions and Models
We can collect data and graph it as a scatter plot or scatter diagram. You have seen
these before in height/weight charts, baby growth charts, loan charts, etc.
Some scatter diagrams can be linear or others will be
Knowing
Section 5.4 Properties of Rational Functions
p x
A Rational Function is a function of the form: R x q x , where p and q
are polynomial functions and q is not the zero polynomial. The domain is
the set of all real numbers except those for which t
Section 5.3 Complex Zeros; Fundamental Theorem of Algebra
When you were doing the last section you worked #28. f x 4 x x x 2 ,
and discovered it had 3 zeros. Graph it and look to see that only one appears on the
graph.
3
2
So, there is only 1 real zero, c
Section 3.5 Graphing Techniques: Transformations
We can get an idea of what a graph looks like by using our knowledge of the
library of functions and transformations.
We will always start with a principle function, meaning one of the library of
functions,
Section 3.2: The Graph of a Function
Remember when we talked about function notation?
f x
is just another notation for y.
f x 2x 3
is the exact same thing as
y 2x 3
x is still the same x variable (the independent
variable),
and f x is the y (dependent var
Section 5.2 The Real Zeros of a Polynomial Function
You have already found zeros of polynomial functionsWhat are other words for
zeros?
What if I asked if 3 is a factor of 105? What would you do?
Remainder Theorem: Let f be a polynomial function. If f(x)
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Radians
Radians are like degrees and are used for measuring angles.
Its an arbitrary distinction, like feet vs meters, except sometimes its better to use one or the
other.
2 radians = 360 degrees
1 radian = 180/ degrees
Degrees to radians-> x degrees = x
Sine, Cosine, Tangent
Sine of angle X is equal to the length of the opposite side (O) divided by the length of the
hypotenuse (H).
Sin(x) = O/H
Cosine of angle x is equal to the length of the adjacent side (A) divided by the length of the
hypotenuse (H).
Section 2.1 . . .basics of functions and their graphs
(some review and some new?)
Go back a step and review some terms from intermediate algebra (or whatever pre-requisite
youve taken):
Relation: A relation is a set of ordered pairs (x,y). It can be a fin
Section 1.6 . . . Solving other types of equations
Not all equations you solve this semester will be quadratic. Some are polynomial equations
degree three or higher, some have rational exponents, and some are best done by a method called
quadratic substit
SECTION 1.5-PART ONE
quadratic equation review
Quadratic equations are any equations which can written in the form ax2 + bx + c = 0 where
a is any real number 0 and b and c are any real numbers, which means they can also be
zero.
You should have covered t
Math 1513
Section 1.5 QUADRATIC EQUATIONS
part two-applications
Thomas Edison was once quoted as saying, Knowledge without application is useless. I
suppose he is right, even though knowing things just for the sake of knowing is pretty fun.
Even so, I agr
Section 2.2 1st and 2nd Derivative Rules
We are now going to investigate the relationship between increasing/decreasing functions and
the derivative rules. These rules will hopefully further reinforce our understanding of how
graphs behave and why they do