Domain and Range Lesson 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.

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Presentation transcript:

Domain and Range Lesson 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?"

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

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

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

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?

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

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

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

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?

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

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

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