Calculus Flashcards
Definition of a function
a function f from a set D to a set Y is a rule that assigns a unique value f(x) in Y to each x in D
Functions are
fundamental to the study of calculus. they are a tool for describing the real world in maths terms. A function can be represented by an equation, a graph, a numerical table, or verbal description.
Domain and range
the value of 1 variable quantity depends on the value of another variable quantity, often called ‘x’. We say “y is a function of x”.
y = f(x) -> (y equals f of x)
The symbols represent
f represents the function,
x represents the independent variable (the input value into y)
y represents the dependent variable or the output value of f at x
The domain
the set D of all possible input values
The range
the set of all possible output values of f(x) as x varies throughout D.
The range might not include every element in the set Y
The natural domain of f
when the domain is not stated explicitly or is restricted by context, the domain is assumed to be the largest set of real x-values for which the function gives real y-values
If you want to restrict a domain in any way
say so explicitly
e.g only positive values for x
y = x^2, x>0
changing the domain
changes the range as well
The range is said to be real-valued when
the range of a function is a set of real-numbers
The domains and ranges of most real-valued functions
are considered intervals or combinations of intervals
a function can have the same
output value for two different input values
a function cannot have the same
input value for two different output values
picture a function as
a machine or as an arrow diagram
