2 - chapter 2 - functions

Question 1

mapping

Answer 1

takes numbers from inputs and assigns them one or more outputs based on mappy rules
eg x -> x^2 + 3, x-> a factor of x

Question 2

represent mapping

Answer 2

using arrow notation eg x -> x^2 + 3
or name the output eg y = x^2 + 3
or use a mapping diagram

Question 3

domain

Answer 3

set of all possible inputs (x)

Question 4

function

Answer 4

type of mapping where each input has one output

Question 5

how to see if something is a function

Answer 5

vertical line test
if a vertical line goes through the function once then its a function if not it isnt

Question 6

how to see if each output comes from one input

Answer 6

horizontal line test
sees if a function is one to one or many to one

Question 7

function types

Answer 7

one to one - every y corresponds to one x
many to one - at least one y that comes from multiple x’s

Question 8

range

Answer 8

set of all possible outputs of a function (y)

Question 9

composite function

Answer 9

eg f(g(x))
g(x) happens then f(the result)
or f^2(x) = f(f(x))
the range of g must lie within the domain of x for the composite function to exist

Question 10

inverse functions

Answer 10

y = f(x)
rearrange to get x
replace every y with x

(reflection of f(x) in the line y = x)
the domain of f-1(x) = the range of f(x) and vice versa - domain and range swap

Question 11

what functions have inverse

Answer 11

one to one functions
have to pass the horizontal line test
- you can restrict a function so its one to one then find the inverse of that to find the inverse of not one to one functions