# 3.3: Function Notation

Difficulty Level: At Grade Created by: CK-12
Estimated17 minsto complete
%
Progress
Practice Function Notation

MEMORY METER
This indicates how strong in your memory this concept is
Progress
Estimated17 minsto complete
%
Estimated17 minsto complete
%
MEMORY METER
This indicates how strong in your memory this concept is

Suppose the value of a digital camera years after it was bought is represented by the function .

• Can you determine the value of and explain what the solution means in the context of this problem?
• Can you determine the value of when and explain what this situation represents?
• What was the original cost of the digital camera?

### Guidance

A function machine shows how a function responds to an input. If I triple the input and subtract one, the machine will convert into . So, for example, if the function is named , and 3 is fed into the machine, comes out.

When naming a function the symbol is often used. The symbol is pronounced as “ of .” This means that the equation is a function that is written in terms of the variable . An example of such a function is . Functions can also be written using a letter other than and a variable other than . For example, and . In addition to representing a function as an equation, you can also represent a function:

• As a graph
• As ordered pairs
• As a table of values
• As an arrow or mapping diagram

When a function is represented as an equation, an ordered pair can be determined by evaluating various values of the assigned variable. Suppose . To calculate substitute:

Graphically, if , this means that the point (4, 8) is a point on the graph of the line.

#### Example A

If find.

a)

b)

c)

Solution:

To determine the value of the function for the assigned values of the variable, substitute the values into the function.

#### Example B

Functions can also be represented as mapping rules. If find the following in simplest form:

a)

b)

c)

Solution:

a)

b)

c)

#### Example C

Let .

a) Evaluate

i)
ii)
iii)

b) Find a value of ‘’ where does not exist.

c) Find in simplest form

d) Find ‘’ if

Solution:

a)

b) The function will not exist if the denominator equals zero because division by zero is undefined.

Therefore, if , then does not exist.

c)

d)

#### Concept Problem Revisited

The value of a digital camera years after it was bought is represented by the function

• Determine the value of and explain what the solution means to this problem.
• Determine the value of when and explain what this situation represents.
• What was the original cost of the digital camera?

Solution:

• The camera is valued at $675, 4 years after it was purchased. • The digital camera has a value of$525, 7 years after it was purchased.

• The original cost of the camera was \$875.

### Vocabulary

Function
A function is a set of ordered pairs that shows a relationship where there is only one output for every input. In other words, for every value of , there is only one value for .

### Guided Practice

1. If find:

i)
ii)

2. If find ‘’ if

3. The emergency brake cable in a truck parked on a steep hill breaks and the truck rolls down the hill. The distance in feet, , that the truck rolls is represented by the function .

i) How far will the truck roll after 9 seconds?
ii) How long will it take the truck to hit a tree which is at the bottom of the hill 600 feet away? Round your answer to the nearest second.

1.

i)
ii)

2.

3.

i)
After 9 seconds, the truck will roll 40.5 feet.
ii)
The truck will hit the tree in approximately 35 seconds.

### Practice

If , find expressions for the following:

If , determine the value of ‘’ when:

The value of a Bobby Orr rookie card years after its purchase is .

1. Determine the value of and explain what the solution means.
2. Determine the value of when and explain what this situation represents.
3. Determine the original price of the card.

Let .

1. When is undefined?
2. For what value of does ?

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

TermDefinition
Function A function is a relation where there is only one output for every input. In other words, for every value of $x$, there is only one value for $y$.

Show Hide Details
Description
Difficulty Level:
Authors:
Tags:
Subjects: