**Functions**

Function Notation

Functional Notation replaces the y in a linear notation with f(x) or f of x as a way to name a function

Equation:

f(x) = mx + b

How to Evaluate a Function

**Wow! Aren't functions great?!?!**

**Function Form of an Equation**

Domain & Range

Domain is the input

Range is the output

In other words, x and y

Re-arranging an equation into Function Notation:

Original equation:

4x + 3y = 12

-4x

-4x

3y = -4x + 12

/3

/3 /3

y = -4/3x + 4

f(x) = -4/3x + 4

How to tell if it is a function with a graph, table, or equation

With a graph you can tell if it is a function by doing the vertical line test

This is not a function because it does not pass the vertical line test

(If there is more than one point on the same vertical line it is not a function)

There are a couple ways to tell if a table is a function or not

You could graph the points and do the vertical line test

or

look at your x coordinates

x

y

Since there is more than one of the same points in the x column it is not a function. -4 and 4 cannot both go in the y column

each value of x can have no more than one value of y

Equation

(not really)

Examples

Is the table a function?

answer: yes

Is the graph a function?

Examples 2

it passes the vertical line test

Is this graph a function?

answer: no

Is the table a function?

answer: yes

There is not more than one y for one x

Coordinates (-1,0) , (-1,-1) do not pass the vertical line test

answer: no

The x point -2 has more than one y value (1.5 and -3.5)

Is the equation linear? Evaluate the function for the given value of x.

answer: yes; -7

Is the equation linear? Evaluate the function for the given value of x.

answer: no; -25

f(x) = x - 11; f(4)

Decide whether a function is linear. Then evaluate the function when x = -2

f(

x

) = -

x

² - 3

x

+5

f(

-2

) = -(

-2

)² - 3(

-2

) + 5

= 7

f(x) is not linear function because it has an x²-term

g(x) is a linear function because it has the form g(x) = mx + b

Write the function

Substitute -2 for x

Simplify

Write the function

Substitute -2 for x

Simplify

g(

x

) = 2

x

+ 6

g(

-2

) = 2(

-2

) + 6

= 2

How to tell if a funtion is linear or not

The equation does not have an x term which makes it linear

The equation does have an x term which makes it not linear

f(x) = -2/3x² - x + 5; f(6)