Functions and Relations

(a) Notation:

Generate ordered pairs { (x₁,y₁), (x₂,y₂), (x₃,y₃)…. }

If the graph passes the VLT, or domain is never the same, then it is a function.

(b) Analysis of the Parabola

 (Standard form)

“a”    Compresses or stretches the parabola
“p”    Translates the parabola positively or negatively by “p” units along the “x” axis.
“q”    Translates the parabola positively or negatively by “q” units along the “y” axis.

(c) Absolute Value Functions:

   Have a characteristic “V” shape.
  
   |x| is always a positive quantity.

(d) Reciprocal of a Function:

   is the reciprocal of

(e) Inverse of a Function:

 is the inverse of
e.g.
 

(f) Adding and Subtracting Function:

   Can only add or subtract functions when their domains are equal

(g) Composition of Two Functions:

This is substituting one function into another.

e.g.  and    

find

Definitions:

as·ymp·tote 
['æszm'tout] n. 
Mathematics. a straight line that continually approaches a curve, but does not meet it within a finite distance. 
D< Gk. asymptohtos < a- not + syn- together + ptohtos apt to fall >

Asymptotes can be vertical,  horizontal or oblique. Asymptotes occur at the zero values of the original function. 

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