Functions Function: a relation between x and y that has the property that no single x value can go to two different y values (______________________________) X:______________________________ Y_______________________________ Implicit form: Explicit form: Function Notation Evaluating a Function f (x) = x 2 + 7 Find f(3a) f(b-­‐1) Compostion of Functions ( f o g)(x) = f (g(x)) is called a compostion of functions. You are plugging one whole function into another function anywhere there is an x. g(x) = cos x f (x) = 2x − 3 find a) ( f o g)(x) b) (g o f )(x) Domain and Range of a function ONLY two situations can affect the domain of a function 1)Any value that will produce a negative inside of an even radical will not be in the domain of the function (take what’s inside the root and set it GREATER THAN OR EQUAL TO ZERO those will be the values in the domain) 2) Any value that will make the denominator of a function ZERO is not in the domain of a function Range is more analytical, for example square root functions will not produce negatives, even power functions will always open up or down limiting their range to that set of values Find the domain of the following 3x
a) f (x) = x − 1 b) f (x) = 2
c) f(x) = tanx x − 2x − 3
Polynomial Vocab Degree:______________________________________________ Leading Coefficient:___________________________________________ Constant Term Even Function: f(-­‐x)=__________________ Odd Function f(-­‐x)=__________________________ Zeros of a function:_________________________________