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econ300 notes - Econ 300 An Introduction to functions What...

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Econ 300 An Introduction to functions What is a Function? A real-valued 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=10-2x y=2x^2 y=sqrt(25-x^2) y=a+bx y=-4-2x+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=10-2x 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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econ300 notes - Econ 300 An Introduction to functions What...

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