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how do you find symmetry about the y and xaxis?
eg.
make y or x equal y and x.
eg.
if the answer is identical to the original formula, it is symmetrical.

how do you find symmetry about the origin?
make both x and y negative.

how can you tell if a function is 1 to 1 or manyto1?
do the horizontal line test

how do you show that a function is not 1to1?
eg.
give two x values that have the same y value.
 vertex: (1, 2)
 yint: (0, 1)
so... f(2) = 1, f(1) = 0

how do you show that a function is 1to1?
eg.
suppose that (the y value at x).
solve both possibilities, eg
and .
Done!

what is an inverse of a function? and how do you prove that two functions are inverse of each other?
an inverse is when (gof)(x) and (fog)(x) both equal (x).
solve both for x. they should both equal x.

how do you find the inverse of a function?
let y=x and x=y.
isolate y and solve for y.
replace y with f(x).

what is
an exponential growth function (with a horizontal asymptote that never touches 0)

what is
an exponential decay function

