, Functions
WHAT MAKES A FUNCTION A FUNCTION?
It is a relationship where every element in the domain (x) and the range (y), where every element of the
domain is associated with one & only one element of the range
1. Vertical Line Test: determines if it is a function or not
IF A VERTICAL LINE CUTS THE GRAPH ONCE THE GRAPH IS A FUNCTION
Function: Not a function:
There are two types of functions:
One to one function: one element of the domain is associated with one element of the range
Many to one function: many elements of the range are associated with the same element of the domain
2. Horizontal Line Test: determines what type of function it is
a. IF THE HORIZONTAL LINE CUTS FUNCTION ONCE = ONE TO ONE FUNCTION
b. IF THE HORIZONTAL LINE CUTS THE FUNCTION MORE THAN ONCE = MANY TO ONE FUNCTION
One to one function: Many to one function:
EXAMPLE:
CONSIDER WHETHER THE GRAPH IS A FUNCTION OR NOT & EXPLAIN
Function, because every element of the domain is associated with one element of the range.
The vertical line test cuts the graph in one place
IF THE GRAPH IS A FUNCTION, STATE THE TYPE AND EXPLAIN
one to one function, because one element of the domain is associated with one element of
the range. The horizontal line test cuts the graph in one place
WRITE DOWN THE DOMAIN AND RANGE
∈
Domain: x R
∈
Range: y R
, Terminology
Definition: rule with two variables
Flow diagram:
input x RULE output y
input: x -> independent variable = domain
output: y -> dependent variable = range
Ordered pair: any point represented by (x;y)
the abscissa: x-coordinate
the ordinate: y-coordinate
DISCRETE CONTINUOUS
continued i.e cant have decimals measured i.e can have decimals
Function Notation NOTE:
method of writing y=3x as f(x) = 3x, where f represents the function IF THERE IS A
f(x) describes the elements of the range of a function FUNCTION WITHIN A
x = independent variable ; f(x) = dependent variable FUNCTION, DO THE
INNER FIRST
EXAMPLE: F(x) = 2x -4
EVALUATE CALCULATE IF F(x) =2 GIVEN FUNCTION: p(x) = 2 - 4x
f (-2) = 2 (-2) -4 2x - 4 =2 Determine the expressions
= -4 -4 2x = 6 2p(x) = 2 (2 - 4x) p(2x) = 2 - 4 (2x)
= -8 x=3 = 4 - 8x = 2 - 8x
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller MogglesStudy. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $4.17. You're not tied to anything after your purchase.