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Note:
1. MDAS
2. the relation of variables
- the output changes only
if the input is changed.
Recall
Formulas that were introduced in the lower grade
level.

Lesson Objectives
1. Identify the difference between a relation and
a function.
2. Demonstrate the steps in evaluating a
function.
3. Illustrate a function through a set of ordered
pairs, table of values, mapping diagram, and
graph.

Definition
A relation is a relationship between sets of
values. The first set of values is called Domain or
the input. The second set is the Range or the
output.

Definition
A function is a relation such that every element
in the domain is paired with exactly one element
in the range.

A function can be illustrated as a machine that
has an input which undergoes a process and
produces an output.
Example.
Machine: Coffee Maker
Input: Coffee Granules
Output: Hot Coffee

1. What is the initial condition for us to have a
function?
2. When is a relation a function?

Representations of a function
A function can be expressed in using set of
ordered pairs, table of values, mapping
diagram, and graph.
Set of ordered pairs
𝑓 = {(1, 3), (2, 5), (4, 6), (7, 9)}.
Note: A function is a relation such that
every element in the domain is paired
with exactly one element in the range.
x , y x , y x , y x , y
x are the inputs. They are the
elements of the Domain
y are the outputs. They are the
elements of the Range

x 1 2 4 7
y 3 5 6 9
x y
Table of Values
Mapping Diagram
Set of ordered pairs
𝑓 = {(1,3), (2, 5), (4, 6), (7, 9)}.
1
2
4
7
3
5
6
9

Definition
A Vertical Line Test is a graph that represents a
function if and only if each vertical line
intersects the graph at most once.

Note: A Vertical Line Test is a
graph that represents a
function if and only if each
vertical line intersects the graph
at most once.

Evaluate the functions by doing the following
simple steps.
1. Replace the variable in the function by the
given value.
2. Simplify by performing the operations.
1. 𝑓 (𝑥) = 3𝑥2
+ 5𝑥 − 8 Solution
a. 𝑥 = −2 f(-2) = 3(-22
) + 5(-2) - 8
= 3(4) – 10 - 8
= 12 - 10 - 8
= -6
-22
= (-2)(-2)
= 4

Evaluate the functions by doing the following
simple steps.
1. Replace the variable in the function by the
given value.
2. Simplify by performing the operations.
2.𝑓(𝑥) = 3𝑥 – 7 Solution
a. 𝑓(5) f(5) = 3(5) – 7
= 15 – 7
= 8

2.𝑓(𝑥) = 3𝑥 – 7 Solution
b. 𝑓(6) f(6) = 3(6) – 7
= 18 – 7
= 11
3. 𝑔(𝑥) = Solution
a. 𝑔(3) 𝑔(3) =
= = =

4. ℎ(𝑥) = Solution
a. h(9) h(9) =
=
=
= 5

Evaluate the functions.
1.𝑓(𝑥) = 3𝑥 – 7 at Solution
a. 𝑓(2.5) f(2.5) = 3(2.5) – 7
= 7.5 – 7
= 7
A function can also be evaluated for a variable input or an
expression input.
b. 𝑓(2𝑟+4) Solution
f(2r + 4) = 3(2r + 4) – 7
= 6r + 12 – 7
= 6r + 5

Evaluate the functions.
3. 𝑔(𝑥) = Solution
a. g(1) 𝑔(1) =
=
= (not possible)
3. ℎ(𝑥) = Solution
a. h(-5) h(9) =
=
=
= 4i (not possible)
Undefined
A fraction with a
denominator of zero.
This means that the x
value of 1 is not in the
domain of the given
function 𝑔(𝑥) =
The square root of a
negative number such as
will result to an
imaginary number of 4i.
This means that the x
value of 9 is not in the
domain of the given
function ℎ(𝑥) =

Lesson 1 - Representations and Evaluation of Functions.pptx

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Lesson 1 - Representations and Evaluation of Functions.pptx

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