Summary of points from lesson on 27 March 2013

Graphs of Standard Functions

(Recap)
Functions are relations
- one to one linear graph
- many to one
- one to many (y^2=x)
- many to many (x^2/a^2 + y^2/b^2 =1) eclipse graph

Functions must be
- logical
- reliable
- reasonable
- predictable

How to test for function (graphically)
- vertical line test
cut once: is a function
cut more than once: not a function
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Linear
- y=kx
- k is the gradient passes through origin
- k>0, sloping up /
- k<0, sloping down \

|k| modulus/ absolute value
- taking the numerical value of k

Quadratic
as |k| increases, the graph becomes narrower

Reciprocal
inverse proportion : y=k/x => xy=k
2 ---(reciprocal)-----> 1/2

when x increase, y decreases
what are values that
x cannot be? -> x≠0
y cannot be? -> y≠0
k cannot be?-> k≠0

At values where x and/or y do not exist, there will be asymptote.

asymptote - a line that continually approaches a given curve but does not meet it at any finite distance.