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Function Notation

Explore f(x) notation for functions

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Function Notation

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 then and explain what this represents?
  • What was the original cost of the digital camera?

Watch This

Khan Academy Functions as Graphs

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
  • As mapping notation

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

Example C

If :

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.

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 mean to this problem.
  • Determine the value of then and explain what this 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, , which 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.

Answers:

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 represents.
  3. Determine the original price of the card.

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