1. Section 1.1 Functions and Change

2. Definition of function
A function is a rule that assigns a unique output to each input
We say that the output is a function of the input
The inputs and outputs are often represented by variables
The set of all inputs is called the domain and the set of all outputs is called the range
A function can be described using words, data in a table, points on a graph, or a formula

3. What are the domain and range of the above function?
Month 1 2 3 4 5 6
Gas
$2.13
$2.16
$2.26
$2.29
$2.41
$2.48
What are the domain and range of the above function?
How can we describe month 3 in function notation?

4. Behavior of Functions Increasing Decreasing Constant Concave Up
Concave Down
Examples: y = x, y = x3, y = ex

5. Linear Functions Has a constant rate of change
Slope
y = f(x) = mx + b where m is the slope and b is the vertical intercept
Now
And is called the difference quotient

6. Delta Notation Δ=“change in”
Slope
Delta Notation Δ=“change in”
Difference Quotient

7. Example
Suppose we know the population of a city is 23,000 in 1982 and 21,000 in 1986
Assuming the population has been declining at a constant rate since 1970, find a formula for the population as a function of time, t
Let t be the number of years since 1970 (i.e. t = 0 corresponds to the year 1970)
Use your model to determine the population in the year 2000
When will the population be 0?