1.2 - Functions and Function Notation
Lesson Outline
Section 1: Do It Now
Section 2: 1.1 Review
Section 3: Find Values Using Function Notation
Section 4: Mapping Diagrams
Section 5: Application of Function Notation
DO IT NOW!
a) State the domain and range of the relation
shown in the following graph:
b) Is this a function?
1.1 Review
What determines if a relation is a function or not?
A function is a relation in which each value of the independent
variable (x) corresponds to exactly one value of the dependent
variable (y)
How does the vertical line test help us determine if a relation is a
function?
For any vertical line that is drawn through a relation, it should
only cross at one point in order to be considered a function.
What is domain?
The set of values x can take.
What is range?
The set of values y can take.
Find Values Using Function Notation
What does a function do?
Takes an input (x), performs operations on it
and then gives an output (y)
What does function notation look like?
f(x) = … something to do with x
Example 1: For each of the following functions,
determine f (2), f (-5), and f (1/2)
What is the value of the function (y-value) when x = 2 ?
a)
f (x) = 2x - 4
b)
f (x) = 3x2 - x + 7
c)
f (x) = 87
Note: f(x) = 87 is a constant function. It is a horizontal line
through 87 on the y-axis.
d)
Mapping Diagrams
A mapping diagram is a representation that can be used when the
relation is given as a set of ordered pairs. In a mapping diagram,
the domain values in one oval are joined to the range values in
the other oval using arrows.
A relation is a function if there is exactly one arrow leading from
each value in the domain. This indicates that each element in the
domain corresponds to exactly one element in the range.
Example 2: Use the mapping diagrams to
i) write the set of ordered pairs of the relation
ii) state if the relation is a function
Since every value in the domain
maps to exactly one value in the
range, this relation is a function.
Since the values x = 2 and
x = 14 both map to more
than one value in the range,
this relation is not a
function.
Applications of Function Notation
Example 3: For the function
i) Graph it and find the domain and range
ii) Find h(-7)
Example 4:
The temperature of the water at the surface of a lake is 22 degrees
Celsius. As Geno scuba dives to the depths of the lake, he finds
that the temperature decreases by 1.5 degrees for every 8 meters
he descends.
i) Model the water temperature at any depth using function notation.
T(d) =
Hint: it is a constant
rate of change,
therefore it will form
a linear relation
(y=mx+b).
ii) What is the water temperature at a depth of 40 meters?
iii) At the bottom of the lake the temperature is 5.5 degrees
Celsius. How deep is the lake?