Relations and Functions: Graphs Flashcards

Relations and Functions

• A relation K can be defined as K = {(x, y) | x - y = 5}.
• For the domain {0, 2, 4}, the corresponding range of y can be found to be {-5, -3, -1}.

Function Criteria

• Set K qualifies as a function as every x value maps to exactly one y value.
• A set of points represents a function if each input (x) is paired with one and only one output (y).

Evaluating Functions

• A graphical representation can help visually assess if a relation is a function.
• Example: A vertical line test is often used; if any vertical line intersects the graph at more than one point, it is not a function.

Specific Examples

• For the points (1,2), (2,1), (3,0), (4,-1), this set does represent a function since there are no repeating x-values.
• If K is defined for the domain of x = 0, 2, and 4, the resulting ordered pairs are (0, -5), (2, -3), and (4, -1).

Function Evaluation

• To evaluate a function at a specific point, such as f(2), the output is determined to be 2 based on the graph of the function.