FUNCTION

1. Concept: Introduction to Functions
EQ: How do we interpret and represent
functions using function notation?
(F.IF.2)
Vocabulary: Function notation, f(x),
Domain, Range
Lesson 3.2 – Function Notation

2. Activating Strategy
Do you have a nickname? If so,
raise your hand to share it with us.
How do you think a nickname and
function notation are related?

3. Introduction
Recall that in a function, every element
of the domain is paired with exactly one
element of the range. That is, for every
value of x, there is exactly one value of y.
Today, we will learn about Function
notation.

4. Introduction, continued
Function notation is a way to name a
function using f(x) instead of y. To make a
general statement, we call the process by a
letter, such as f, and we can call the results
of that process “f of x.” We write “f of x” as
f(x).
Functions can be named using any letter,
though f and g are used often. Using function
notation, we can graph more than one
function at a time. If we call one function f
and another g, then we can graph y = f(x)
and y = g(x) on the same coordinate plane.

5. Key Concepts
Functions can be evaluated at values
and variables.
To evaluate a function, substitute the
values for the domain for all occurrences
of x.
To evaluate f(2) in replace all x’s with 2
and simplify: .This means that .
 is an ordered pair of a function and a
point on the graph of the function.

6. Key Concepts, continued
For example, let f be a function with the
domain {1, 2, 3} and let f(x) = 2x. To
evaluate f over the domain {1, 2, 3}, we
would write the following equations by
substituting each value in the domain for x:
f(1) = 2(1) = 2
f(2) = 2(2) = 4
f(3) = 2(3) = 6
{2, 4, 6} is the range of f(x).

7. Steps for Evaluating Functions
Step 1: Evaluate the function
over the domain by substituting
the values from the domain into
the function.
Step 2: Collect the set of outputs
from the inputs. (Your answers
from step 1 will become your
outputs, or range).

8. Example 1:
Evaluate over the domain .
What is the range?
To evaluate over the domain ,
substitute the values from the
domain into .

9. Example 1, continued
1)Evaluate
Original function
Substitute 1 for x.
Simplify.
2)Evaluate .
Original function
Substitute 2 for x.
Simplify.

10. Example 1, continued
3) Evaluate
Original function
Substitute 3 for x.
Simplify.
4) Evaluate .
Original function
Substitute 4 for x.
Simplify.

11. Example 1, continued
The range is

12. You Try!
1. for the domain
.

13. Example 2
Complete the input-out table for
the function .

14. Example 2, continued
Step 1: First we will evaluate and .
Substitute the values into our
equation:

15. Example 2, continued
 Evaluate .
Original function
Substitute -1 for x
Simplify.
 Evaluate .
Original function.
Substitute 3 for x.
Simplify.

16. Example 2, continued
Step 2: Plug these values into our table.
&
How can we find the other values?

17. Example 2, continued
Step 3: We need to find when and when To do
this, we need to set the equation equal to our
given values.
 Set equal to
Original function.
Subtract 5 from each side.
Divide both sides by -3.

18. Example 2, continued
Step 3 (Continued):
Original function.
Subtract 5 from each side.
Divide both
sides by -3.

19. Example 2, continued
Step 4: Plug these values into our table.
&

20. You Try!
2. Complete the input-output table for
the function .

21. Example 3
Look at the
graph of , what
is ?
Hint: Use what
you know about
function notation
and graphing
functions.

22. You Try!
Look at the
graph of , what
is ?

23. Example 4
Cindy has a steady babysitting job.
The total charge for a babysitting
job can be represented by the
function , where t is the number of
hours. Evaluate c(5) and
interpret the results.

24. You Try!
4. The local Italian restaurant has had a
steady increase in customers and is,
therefore, hiring people at a steady rate.
The function of the increase in employees
is , where x is in months. Evaluate and
interpret the results.

25. Summary: 3-2-1
List 3 main things you know
about function notation,
give 2 examples of function
notation, and 1 question
you have about function
notation.