Functions (MCR3U - Functions)

what is a relation

-two y values

-if coordinates given and there are x values with different y values, it is a relation

one to one relation

one element of the domain corresponds to only one element in range

one to many relation

at least one element in the domain correspond to more than one element of the range.

Many to one relation

more than one element in the domain correspond to one element of the range

Which of the following are functions:

Many to one relation

one to many relation

one to one relation

one to one

many to one

write the interval notation of this

{x | −3≤x≤1}

[−3,1]

write the interval notation of this

{x | −3<x<1}

(−3,1)

write the interval notation of this

[−2,4)

write the interval notation of this

[−4,−2]∪(−1,1)∪(1,2]∪{4}

what is a asymptote

a line that a curve approaches but never touches or crosses

what does discrete mean

describes graphs where either the domain or range contains individual points

what parent function is this

f(x)=x²

what does the parent function f(x)=x² look like? Main points?

x= 1,2,3

what parent function is this

f(x)=|x|

what would the parent function f(x)=|x| look like? main points?

x=-3,-2,1,1,2,3

what parent function is this?

f(x)=√x

How would you graph f(x)=√x? Main Points?

x=0,1,4,9

What parent function is this?

f(x)=1/x

How would you graph f(x)=1/x ? Main points?

x=-2, -1, -0.5, 0.5,1,2

what is the formula for function transformation

y - af(k(x - d)) + c

Which part y=af(k(x - d)) + c is vertical translations?

c is

• c>0 shift up

• c<0 shift down

Which part y=af(k(x - d)) + c is horizontal translations?

d is

• d>0 right

• d<0 left

Which part y=af(k(x - d)) + c is horizontal stretch/compression?

k is

• k>1 or k< -1 compressed horizontally by 1/k (x/k)

• -1<k<1 stretched horizontally by 1/k (kx)4

• k<0 horizontal reflection (y axis)

How would you graph this transformation:

y=4f[-1/2x-3]-5

What is the mapping notation formula?

(X/k+d,ay+c)

Which type of map is the inverse of a function of?

A one-to-one

How do you say f^-1 in words

Inverse of f

f^-1(x)

f inverse of x

How do you say f(1)=-2

F of 1 is equal to -2

What is the inverse of a relation represent?

describe function

write equation

graph using function notation.

determine equation

determine the equation: