2.1 Basic of Functions and Their Graphs
Function (True or FALSE)
A relation is not a function when two different ordered pairs have the same first component and different second components.
Domain
First components of the ordered pairs. [x]
The Vertical Line Test for Functions
If any vertical line intersects a graph in more than one point., the graph does not define y as a function of x.
graph of a function
graph of its ordered pairs.
Function (def)
is a correspondence from a first set. called the domain, to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range.
Function
is a relation in which no two ordered pairs have the same first component and different second components.
Which of the following statements defines a function?
is a set of ordered pairs in which each first component in the ordered pairs corresponds to exactly one second component.
Graph of a function
is the graph its ordered pairs.
f (x)
read "f of x" or "f at x" represents the value of the function at the number of x.
FOIL
...
Function (TRUE or False)
A function can have more than one x-intercept but at most one y-intercept.
Intercepts
A function can have more than one x-intercept but at most one y-intercept.
True or FALSE
A function can have more than one y-intercept.
Function (TRUE or False)
A function can have two different first components with the same second component.
Vertical Line Test
A test that determines whether a graph defines y as a function of x.
Range
All Second Components of ordered pairs [y]
Relation
Any set of ordered pairs
Closed Dot (Graphs)
Indicates that the graph does not extend beyond this point and the point belongs to the graph.
Open Dot (Graphs)
Indicates that the graph does not extend beyond this point and the point does not belong to the graph.
An Arrow (Graphs)
Indicates that the graph extends indefinitely in the direction in which the arrow points.
Dependent Variable
Variable y, because its value depends on x
TRUE or False
When giving the Domain and Range of the relation, you do not need to list duplicate number. {(3,1),(3,9),(7,1),(7,9)}
Function
a relation in which each member of the domain corresponds to exactly one member of the range.
Linear functions
all functions with equations of the for f(x) = mx + b graph as straight lines.
Zeros of a Function
are the x-values for which f(x)=0. Thus, the real zeros are the x-intercepts.
Function (TRUE or False)
are usually given in terms of equations rather than as sets of ordered pairs.
The notation f(x) describes
the value of f at x.
Independent Variable
variable x, because it can be assigned any value from the domain.