Function Rule/Function Notation

Function Rules

Learning Intentions:
I can use a rule or a "function" to evaluate expressions.
I can know that the INPUTS are the "x's" or the DOMAIN values.
I can know that the OUTPUTS are the "y's" or the RANGE values.

Evaluating Functions

To EVALUATE a Function is to: Replace (substitute) its variable with a given number or expression

Multiple Choice

I am on the X axis and I am the input

• Domain

• Range

• Neither

• Both

Multiple Choice

I am on the Y axis and I am the output

• Domain

• Range

• Neither

• Both

Multiple Choice

REVIEW PROBLEM from the past:

Given y = 2x + 1, find the value of y when x = 5

• 9

• 10

• 11

• 24

Multiple Choice

Evaluate y = 7x when x = -5

• -35
• 35
• 2
• 75

Multiple Choice

SAME QUESTION: Only now we REPLACE the "y" with "f(x)"

Evaluate f(x) = 7x when x = -5 or when you replace it becomes f(-5) = 7(-5)

• -35
• 35
• 2
• 75

Multiple Choice

Evaluate f(x) = x + 5 when x = 10.

• 5

• 20

• 1/2

• 15

Function Notation

A concise way of substituting specific values for x

Written: f(x) (used to be "y")

Read: "f of x"

Multiple Choice

How do you read f(x)?

• f x

• f of x

• f parenthesis x

• f with an x inside parenthesis

Evaluating Functions

y = 2x - 1 is a function.

So it can be written in function notation.

f(x) = 2x - 1

​

​

The questions we answered

Given y = 2x - 1, find the value of y when x = 5.

​

Can be asked this way

Given f(x) = 2x - 1, find f(5).

EXAMPLE​

​Given f(x) = 4x - 9, find f(2)

​Say ...f "of" 2 means to let x = 2 and substitute 2 in place of x.

f(2) = 4(2) - 9
f(2) = 8 - 9
f(2) = -1

means the ANSWER or OUTPUT is -1 when the INPUT or DOMAIN value was =2.
Basically FUNCTION NOTATION shows more information

Multiple Choice

Given f(x) = -3x + 5, find f(2).

...means f(2) = -3(2) + 5

• f(2) = -1

• f(2) = -11

• f(2) = 11

• f(2) = 1

Multiple Choice

If a question asks you to find f(2), what does that mean?

• Let x = 2

• Let y = 2

Multiple Choice

g(x) = 3x + 1
Which is correct substitution for g(2) = ?

• 3(6) + 1

• 3(2) + 1

• 3(g)+1

Multiple Choice

g(x) = 3x + 1
g(2) = _______

• 6
• 7
• 8
• 9

Multiple Choice

f(x) = x² + 7
x(2) = ______

• 10
• 11
• 13
• 12

Fill in the Blanks

Given f(x) = -x + 12, find f(-2).

Fill in the Blanks

Given f(x) = -x + 6x + 8, find f(-6).

Fill in the Blanks

Given f(x) = -5x - 15, find f(4).

Evaluate a Function

From Graphs

Evaluate from Graphs

• Are you finding x or y?

• If it's f(#) you are finding y and know what x is

• If it's f(x) = # you are finding x and know what y is

Evaluating Functions: Graphs

We have seen how to evaluate functions from:

• ​​Equations

• ​Tables

• ​Ordered Pairs

• ​Mapping Diagrams

​​Today, we are going to be looking at how to evaluate functions from graphs!

​If we were evaluating a function and got

​what would this be as an ordered pair?

​The number in the parenthesis, 3, is the x value and f(3) is the y value!

​When we are evaluating functions from graphs, we want to pay attention to what the y-value is for the given x value, which we find in parentheses

​Now, let's find !

Multiple Choice

With this in mind, try to find  $$f\left(4\right)$$  from this graph, 

• 4

• -5

• -6

• 1

What if we were asked to find x when f(x)=-5

Multiple Choice

Use the graph to find  $$x$$  when  $$f\left(x\right)=-2$$  

• 6

• 5

• -7

• 0

Multiple Choice

Use the graph to find  $$f\left(1\right)$$  

• 6

• 5

• -7

• 0

Multiple Choice

Use the graph to find  $$x$$  when  $$f\left(x\right)=-5$$  

• 6

• 5

• -7

• 3

Multiple Select

Given the graph of g(x), evaluate: g(x) = 0.

Select all that apply.

• -5

• -4

• 2

• 3

• 6

Multiple Select

Given the graph of g(x), evaluate: g(x) = 2.

Select all that apply.

• -5

• -3

• 3

• 7

Fill in the Blanks

Given the graph of function f, evaluate f(3) =

Fill in the Blanks

Given the graph of function f, evaluate f(x) =2

Multiple Choice

Looking at the graph, what is the value of t for the function: f(t) = 15?

• t = 5

• t = 15

• t = 25

Multiple Select

What is x if
f(x) = -3?

• -3

• -4

• -5

• 2

• 0