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MATH 1113 Precalculus 2.1 notes
A ___________ is a correspondence between ____________. If x and y are two ____________ in these ______ and if a ___________ exists between x and y , then we say that x corresponds to y or that y ____________ on x.
Maps and Ordered Pairs as Relations
Definitions: Let X and Y be two nonempty sets of real numbers. A _____________ from X into Y is a relation that associates with each element of X ___________________________ element of Y. The set X is called the _______________ of the function. For each element x in X , the corresponding element y in Y is called the image of x. The set of all images of the elements of the domain is called the _____________ of the function.
FUNCTION ?
Determine whether each relation represents a function. If it is a function, state the domain and range.
Determine if the equation defines y as a function of x.
(^1 ) y = − 2 x −
Determine if the equation defines y as a function of x.
x = 2 y^2 + 1
Function Notation
y = f ( x )
___ is a symbol for the function
___ is the _________________ variable
___ is the _________________ variable
___ is the value of the function at ____
If f and g are functions, their sum __________ is the function given by
The domain of f + g consists of the numbers x that are in the domain of f and in the domain of g. If f and g are functions, their difference _____________ is the function given by
The domain of f - g consists of the numbers x that are in the domain of f and in the domain of g. Their product _____________ is the function given by
The domain of f • g consists of the numbers x that are in the domain of f and in the domain of g. Their quotient ________ is the function given by
The domain of f / g consists of the numbers x for which g ( x ) ≠ 0 that are in the domain of f and in the domain of g.
Example: For the functions f ( x )= 2 x^2 + 3 and g ( x )= 4 x^2 + 1 find the following:
a.) ( f + g) (x) b.) ( f - g) (x)
c.) ( f • g) (x) d.)
More practice with the difference quotient and domain:
Find the domain and difference quotient
h
f ( x + h )− f ( x )of the following functions.
( f / g )( x )
2.1 Assignment 1-14 ALL, 15-25 Odd, 27, 33, 39, 41, 43, 44, 45, 47-59 Odd, 61, 67, 71, 73-80 ALL, 81, 83
2
) ( )^1
) ( ) 4 2 5 7
=
= + −
x
b f x
a f x x x
