Function Notation

Function Notation

A concise way of substituting specific values for x

Written: f(x)

Read: "f of x"

Think of a function like a machine ...

• Substitute "in" value for x (or other variable)

• Calculate "out" value using Order of Operations

Think of a function like a machine ...

• Substitute "in" value for x (or other variable)

• Calculate "out" value using Order of Operations

• This example is showing f(x)=5x + 1

• This is read f (of x) = 5x plus 1

• So, with function notation, the y is replaced with f(x).

Function Machine

You will also see this type of function machine.

You can see that x is being put into the machine, and f(x), which is the output, is coming out.

Multiple Choice

Let's Try it:

If the input is -3, determine the corresponding output.

• f(x) = -2

• y = -2

• f(x) = 10

• y =10

Example 1

Here, we're told that our rule is

f(x) = -2x +4 and that x is equal to -3.

When we input -3 into our equation, we get an output of 10.

Make sure you are using FUNCTION NOTATION. f(-3) = 10. This is read f of -3 equal 10.

Multiple Choice

Find f(x) if x=-2.

• f(x)=9

• f(x)=-15

• f(x)=-9

• f(x)=21

Multiple Choice

f(5) = ?

• 25

• 125

• 5

• 10

Multiple Choice

Find the output.

• 17

• 55

• 30

• 37

Multiple Choice

• 16

• 48

• -28

• 4

Multiple Choice

Find the input of this function machine.

• -2

• 1

• 8

• No Solution

Multiple Choice

Given f(x) = -4x - 10 and f(x) = 10. Find x

• x = -5

• x = 5

• x = -50

• x = 30

Determining "in" and "out" from a graph

• A graph is a set of ordered pairs (x, y)

• x is always the "input"

• f(x) - also called y - is always the "output"

• So, we can identify x and y in a graph and determine the function values!

Poll

What is x if

f(x) = -2?

• 4

• 3

• 0

• 8

 What is x if f(x) = -2?

First, we need to locate -2 on the Y axis. REMEMBER, that f(x) = -2 is the same as y = -2.

So the question as, when y = -2, what does x =?

When y = -2, x is equal to 8.

Multiple Choice

What is f(1)?

• 1

• 5

• 0

• 4

Multiple Choice

What is f(8)?

• 8

• 0

• 3

• -2

Poll

How comfortable are you with function notation? Choose the color based on your answer.

• Red

• Yellow

• Green