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 ReviewWhat determines if a relation is a function or not?

How does the vertical line test help us determine if a relation is a function?

A function is a relation in which each value of the independent variable (x) corresponds to exactly one value of the dependent variable (y)

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?

What is range?

The set of values x can take.

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)

a) f (x) = 2x - 4

What is the value of the function (y-value) when x = 2 ?

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 relationii) 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)

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.

Example 4:

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?