functions and graphs

what is the domain of a function?

the set of all possible inputs for a mapping

what is the range of a function?

the set of all possible outputs for the mapping

what does a mapping do?

transform one set of numbers into a different set

how can a mapping be represented?

• in words

• algebraic equation

• graph

when is a mapping a function?

if each input has a distinct output

what types of mapping are there?

• one to one function

• many to one function

• not a mapping

HERE

what is a real number?

any number that isn’t a complex number

what is a complex number?

a number that includes both a real number and an imaginary number

what is an imaginary number?

a number that does not exist, e.g., i

how do you solve f(x) = f^-1(x)?

they intersect at y = x, so when f(x) = x. therefore you do x = f^-1(x). you can see whether your answer is positive or negative by looking at the graph

how do you find an inverse function?

1. change f(x) into y

2. switch the y and x

3. rearrange for y

4. switch the values back, y = f^-1(x), x = x

for an inverse function, is y or x in the domain? why?

x and idk

for an inverse function, is y or x in the range? why?

y and idk

what does an inverse graph look like plotted with the regular function?

• same but opposite, with the point of intersection at y = x

• y-int of f(x) = x-int of f^-1(x), and vice versa

GRAPH EXAMPLE

f(x) = 4 - x

f^-1(x) = 4 - x

what is the difference?

range and domain values are different, because f(x) range = f^-1(x) domain and vice versa