Relations and Functions: Graphs Flashcards

If K = {(x, y)|x - y = 5}, find the corresponding range of y for the domain {0, 2, 4}.

If K = {(x, y) | x - y = 5}, is Set K a function?

Do the set of points in the figure represent a function?

Do the set of points in the figure represent a function? (1,2), (2,1), (3,0), (4,-1)

For K = {(x, y) | x - y = 5}, what are the output pairs when the domain of x is 0, 2, 4?

Use the graph of the function to evaluate f(2).

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.

This quiz provides flashcards focusing on relations and functions, specifically through graphs. It will test your understanding of function definitions, domains, and ranges through various questions and scenarios.