Functions ●Vhat is a function? OHow does a function play in Calculus? oWhat is any difference between the function in Calculus and the Mathematics in the Middle School?
Functions ⚫What is a function? ⚫How does a function play in Calculus? ⚫What is any difference between the function in Calculus and the Mathematics in the Middle School?
Basic Concepts ●Variables:x,y ●Value or image oRelation ●Determination ●Region
Basic Concepts ⚫Variables: x,y ⚫Value or image ⚫Relation ⚫Determination ⚫Region
Definition of Function If a variable y depends on a variablex in a such way that each value of x determines exactly one value of y,then we say thaty is a function ofx. OA function fis a rule that associates a unique output with each input.If the input is denoted by x,then the output is denoted byfx)(read“fofx")
Definition of Function ⚫If a variable y depends on a variable x in a such way that each value of x determines exactly one value of y, then we say that y is a function of x. ⚫A function f is a rule that associates a unique output with each input. If the input is denoted by x, then the output is denoted by f(x) (read “f of x”)
Represent of Function Numerically by tables Geometrically by Graphs oAlgebraically by formulas ●Verbally
Represent of Function ⚫Numerically by tables ⚫Geometrically by Graphs ⚫Algebraically by formulas ⚫Verbally
Example of Function 1 0 1 2 3 f(x) 3 4 -1 3 f(0)=3,f(1)=4, f(2)=-1,f(3)=3
Example of Function 1 x 0 1 2 3 f (x) 3 4 -1 3 (0) 3, (1) 4, (2) 1, (3) 3 f f f f = = = − =