1. Today’s Topics: Function Notation Domain & Range Recognizing Functions
1.1 Functions and Models
Today’s Topics:
Function Notation
Domain & Range
Recognizing Functions

2. Definition
Function: A function is a rule or correspondence that assigns to each element of one set exactly one element of a second set.
The function may be defined by a set of ordered pairs, a table, a graph an equation or a verbal description.

3. Part I – Function Notation
Ex 1 – Function Notation with Equations
Evaluate the following expressions given the functions below:
g(x) = -3x + 1 f(x) = x 𝐡 𝐱 = 𝟏𝟐 𝐱
a. g(10) = b. f(3) = c. h(–2) =
d. f(-7) = e. h(4) = f. g(-5) =

4. Ex 2: Function Notation with a Graph
f(x) y x 5 -5
Find:
f(–4) =
f(0) =
f(3) =
f(-5) =

5. Ex 3: Mortgage
Mortgage A couple can afford $800 per month to purchase a home. As indicated in the table, if they can get an interest rate of 7.5%, the number of years that it will take to pay off the mortgage is a function of the dollar amount A of the mortgage for the home they purchase.
Amount A ($)
t (years)
40,000 5
69,000 10
89,000 15
103,000 20
120,000 30
If the couple wishes to finance $103,000, for how long must they make payments? Write this in function form if t = f(A).
What if f(120,000)? Write a sentence that explains its meaning.
What is f(3∙40,000)?
What value of A makes f(A) = 5 true?
Does f(3∙40,000) = 3 ∙ f(40,000)? Explain your reasoning.

6. Part II – Domain & Range Definition
Domain: The domain of a function is the set of all possible input values (usually x), which allows the function formula to work
Definition
Range: The range is the set of all possible output values (usually y), which result from using the function formula.

7. Ex 1: Relationship between Celsius and Fahrenheit
Celsius Degrees
-20
-10 -5 25 50
100
Fahrenheit Degrees -4 14 23 32 77
122
212
Using the table above, determine the domain and the range.

8. Ex 2: Write the domain and range of each function.
D: D:
R: R:

9. Ex. 3: Domain and Range
For each of the following functions, determine the domain. Determine the range of each function.
y = 𝑥 2 +5
𝑓(𝑥)=2+ 1 2𝑥−5
𝑔(𝑥)= −3𝑥
Determine the domain and range of this function.
𝑥 2 + 𝑦 2 =25

10. Part III – Recognizing Functions
Recall that a function is a rule or correspondence that assigns to each element of one set (called the domain) exactly one element of a second set (called the range). The function may be defined by a set of ordered pairs, a table, a graph, an equation or a verbal description.

11. Ex. 1: Determine whether or not the indicated relationship represents a function.Y
-100 5
109 10
480 15
505 20 25 30
. Does the table describe y as a function of x? Why or why not?
Does the equation 𝑦 2 =5𝑥−5 define y as a function of x?

12. Recognizing Functions
Definition
Vertical Line Test: A set of points in a coordinate plane is a the graph of a function if and only if no vertical line intersects the graph more than one point.
Examples on the white board.

13. Assignment
Pg #3-17 odd #26 #28 #29-33 all #49 #66