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Domain and Range

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)

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Domain and Range

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  1. Domain and Range Lesson 2.2

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

  3. Definition Given a function Q = f(t) • DomainThe domain of f is the set of all possible input values, t, which yield an output • RangeThe 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 anda 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: -1.19 ≤ y < 0 excluded

  13. Assignment • Lesson 2.2 • Page 72 • Exercises1, 3, 5, 9, 13, 19, 23, 27, 31, 33, 35

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