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.

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