1. Domain and Range
Lesson 2.2

2. Home on the Range What kind of "range" are we talking about?
What does it have to do with "domain?"
Are domain and range really "good fun for the whole family?"

3. Definition Given a function Q = f(t)
Domain The domain of f is the set of all possible input values, t, which yield an output
Range The range of f is the corresponding set of output values Q

4. Domain
The domain is the set of all possible inputs into the function { 1, 2, 3, … }
The nature of some functions may mean restricting certain values as inputs

5. Range
{ 9, 14, -4, 6, … }
The range would be all the possible resulting outputs
The nature of a function may restrict the possible output values

6. Choosing Realistic Domains and Ranges
Consider a function used to model a real life situation
Let h(t) model the height of a ball as a function of time
What are realistic values for t and for height?

7. Choosing Realistic Domains and Ranges
By itself, out of context, it is just a parabola that has the real numbers as domain and a limited range

8. Choosing Realistic Domains and Ranges
In the context of the height of a thrown object, the domain is limited to 0 ≤ t ≤ 4 and the range is 0 ≤ h ≤ 64

9. Using a Graph to Find the Domain and Range
Consider the function
Graph the function to determine realistic values for domain and range

10. Using a Graph to Find the Domain and Range
Zoom in or out as needed
Check resulting window setting
What domain and range do you conclude from the graph?

11. Using a Formula to Find Domain and Range
Consider the rational function
Looking at the formula it is possible to see that since the denominator cannot equal zero, we have a restriction on the domain

12. Using a Formula to Find Domain and Range
Consider what happens to a function
when a denominator gets close to zero
when x gets very large
Then we have an idea about the range of a function
Range: ≤ y < 0 excluded

13. Assignment Lesson 2.2 Page 72
Exercises 1, 3, 5, 9, 13, 19, 23, 27, 31, 33, 35