Függvények, tartomány és értékkészlet

Functions, Domain, and Range

• A function is a relation where each x-value has only one y-value. Functions can be represented in various ways: words, tables, ordered pairs, set notation, mapping diagrams, graphs, or equations.
• The vertical line test determines if a relation is a function. If a vertical line drawn anywhere through the graph intersects the graph only once, the relation is a function.
• Domain: All valid x-values in a relation.
• Range: All valid y-values in a relation.
• Asymptote: A line that a curve approaches but never touches. An example is y = 2x + 1, the horizontal asymptote is the line y = 1.

Function or Not?

• Relations can be analyzed to determine if they are functions.
• Tables of x and y values are used to determine if a relation is a function. If each x value maps to only one y value, then it is a function.
• Ordered pairs are used to determine if a relation is a function. A relation made of ordered pairs is a function if each x value is only paired with one y value.
• Graphs are used to determine if a relation is a function, and to determine the domain and range. The vertical line test is used to check if a graph is a function.

Domain and Range from Graphs

• Domain and range can be determined from graphs using interval notation or set notation.
• Domain represents the valid x values on a graph, range represents the valid y values.
• Examples provided showcase how to find the domain and range of various functions from their graphs. Graphs of functions and relations are illustrated.

Additional Concepts

• Identifying functions from tables, ordered pairs, and graphs is key.
• Determining the domain and range from different representations of relations is essential.
• Asymptotes in functions and graphs are addressed.