Notes on Domain and Range

Topic: Domain and Range Match Up

Introduction to Domain and Range

• Definition of Domain: The domain of a function is the complete set of possible values of the independent variable (input).

• Definition of Range: The range of a function is the complete set of possible values of the dependent variable (output) that result from using the function.

Importance of Domain and Range

• Understanding the domain and range is crucial for accurately graphing functions and equations.

• It allows for better comprehension of the behavior of functions in various contexts, including real-world applications.

Key Concepts

• Independent Variable: The variable that represents the input of a function, usually denoted as 'x'.

• Dependent Variable: The variable that represents the output of a function, usually denoted as 'y'.

Examples of Domain and Range

• For a linear function, such as $y = 2x + 3$:

  • Domain: All real numbers, represented as $(- ext{∞}, + ext{∞})$.

  • Range: All real numbers, also represented as $(- ext{∞}, + ext{∞})$.

• For a quadratic function, such as $y = x^2$:

  • Domain: All real numbers, represented as $(- ext{∞}, + ext{∞})$.

  • Range: All non-negative real numbers, represented as $[0, + ext{∞})$.

• For a rational function, such as $y = \frac{1}{x}$:

  • Domain: All real numbers except for zero, represented as $(- ext{∞}, 0) \cup (0, + ext{∞})$.

  • Range: All real numbers except for zero, represented as $(- ext{∞}, 0) \cup (0, + ext{∞})$.

Visual Representation

• The domain and range can be graphically represented using function graphs, where the x-axis corresponds to the domain and the y-axis corresponds to the range.

Matching Domain and Range

• The activity suggested is likely to involve matching specific domains with their corresponding ranges based on given functions. This reinforces the understanding of the interplay between inputs and outputs in mathematical functions.