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48 Cards in this Set

  • Front
  • Back

Relation

a set of ordered pairs

Function

A relation where each x has only one y.


- passes the vertical line test


- x's don't repeat

Domain

The first element (x's) or independent variable


- how wide the graph gets (use only 'x' numbers)

Range

The second element (y or f(x)) or dependent variables


- how high or low the graph gets (use only 'y' numbers)

One-to-One Function

Every element of the range (y) of the function corresponds to exactly one element of the domain (x).


- Passes the vertical and horizontal line test.


- neither x's nor y's can repeat

What is the domain?


 

What is the domain?


What is the domain? 

What is the domain?

x > 3

What is the domain?

What is the domain?

15

Find h(0) - h(2)

Find h(0) - h(2)

-2

Find x if h(x) = 3

Find x if h(x) = 3

0

Find x if h(x) = 2

Find x if h(x) = 2

-1

Is this a function?

Is this a function?

no - anything with y squared can't be a function

Is this a function?

Is this a function?

yes

Is this a function?

Is this a function?

yes

Is this a function?

Is this a function?

yes

Is this function onto?

Is this function onto?

no

Is this function onto?

Is this function onto?

yes

Is this function onto?

Is this function onto?

no

Is this relation a function?

Is this relation a function?

yes

State the domain

State the domain

(-3,2]

State the range

State the range

-1,1

is a function if f(x) is what ?

is a function if f(x) is what ?

One to One

State the domain

State the domain

[0,infinity)

Is this a function?

Is this a function?

No

State the range

State the range

Is the inverse a function?

Is the inverse a function?

Yes (It is One to one)

Is this relation onto?

Is this relation onto?

Yes

Given the relation:


{(2,1),(2,2),(2,3),(2,4)}


Is it a function?

No

Given the relation:


{(2,1),(2,2),(2,3),(2,4)}


State the domain

2

Given the relation:


{(2,1),(2,2),(2,3),(2,4)}


State the range.

{1,2,3,4}

Given the relation:


{(2,1),(2,2),(2,3),(2,4)}


State the inverse.

{(1,2),(2,2),(3,2),(4,2)}

Given the relation:


{(2,1),(2,2),(2,3),(2,4)}


Is the inverse a function?

yes

 


What is f(-2)


What is f(-2)

18

Find f(g(-3))

Find f(g(-3))

18

Find g(f(x))

Find g(f(x))

x

2

The graph of any function and its inverse are symmetric with respect to _______________

The line y = x

To find the inverse of a function simply__________

Switch the x and the y

f(x) is the parent function


What would f(x) + 2 do to the function?

Move it up 2

f(x) is the parent function


What would f(x) - 4 do to the function?

Move it down 4

f(x) is the parent function


What would f(x-4) do to the function?

Move it to the right 4

f(x) is the parent function


What would f(x + 5) do to the function?

Move it to the left 5

f(x) is the parent function


What would -f(x) do to the function?

Reflect it through the x-axis

f(x) is the parent function


What would f(-x) do to the function?

Reflect it through the y-axis

Given the parent graph: f(x) = |x|


What is the transformation that created


g(x) = |x + 2| - 3?

Moved down 3 and to the left 2.

Onto

The range is all real numbers.