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Econ 300
An Introduction to functions
What is a Function?
A realvalued function is a rule that assigns a real number to one or more other real numbers
A mapping or transformation that associates each element from a set x to elements in a set y
f: x>y
Why are functions useful?
A function f describes the relation between the variables in sets x and y
Types of functions: Univariate Functions
If x is a variable that represents a real number, the univariate function “f” maps or transforms the value
x into some value y
f: x>y or y=f(x)
The variable x is said to be the domain of the function while y is its range
The variable x is also called the independent variable while y is the dependent variable
note that formation y=f(x) is also called an equation
Examples of univariate function
y=102x
y=2x^2
y=sqrt(25x^2)
y=a+bx
y=42x+2x^2
what type of economic relationships do these functions describe?
Is there some other way to look at functions?
Graphing helps visualize the relation of behavior of a function
Example: plot the function y=102x on the XY axis using analytic geometry
Step 1: Pick some values of x and calculate
Types of functions: Multivariate functions
the domain x need not be a single number
the domain of a function may be a collection of n variables (x1, x2,.
..xn)
Examples of multivariate functions
c=300+.06l+.02w
y=3x^(1/2)x^(1/2)
what types of economic relations could there functions derive
how can we graph multivariate functions?
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 Spring '08
 cramton

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