Domain In a set of ordered pairs x

Domain: In a set of ordered pairs, (x, y), the domain is the set of all x-coordinates. Range: In a set of ordered pairs, (x, y), the range is the set of all y-coordinates.

The set of ordered pairs may be a limited number of points. Given the following set of ordered pairs, find the domain and range. Ex: {(2, 3), (-1, 0), (2, -5), (0, -3)} Domain: {2, -1, 0} Range: {3, 0, -5, -3} If a number occurs more than once, you do not need to list it more than one time.

The set of ordered pairs may be an infinite number of points, described by a graph. Given the following graph, find the domain and range.

Domain: {all real numbers} Range: {y: y≥ 0}

The set of ordered pairs may be an infinite number of points, described by an algebraic expression. Given the following function, find the domain and range. Example: Domain: {x: x≥ 5} Range: {y: y≥ 0}

Practice: Find the domain and range of the following sets of ordered pairs. 1. {(3, 7), (-3, 7), (7, -2), (-8, -5), (0, -1)} Domain: {3, -3, 7, -8, 0} Range: {7, -2, -5, -1}

2. Domain={x: x } Range: {all reals}

3. Domain={all reals} Range: {y: y≥-4} 4. Domain={x: x≠ 0} Range: {y: y≠ 0}

5. Note: This is NOT a Function! Domain={x: -2≤x≤ 2} Range: {y: -2≤y≤ 2} 6. Domain={all reals} Range: {all reals}

Choosing Realistic Domains and Ranges � Consider situation � Let a function used to model a real life 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 � 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

Using a Formula to Find Domain and Range � Consider � Looking the rational function 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: -1. 19 ≤ y < 0 excluded