Questions and Answers
If K = {(x, y)|x - y = 5}, find the corresponding range of y for the domain {0, 2, 4}.
{-5, -3, -1} or {0, 2, 4}
If K = {(x, y) | x - y = 5}, is Set K a function?
True
Do the set of points in the figure represent a function?
False
Do the set of points in the figure represent a function? (1,2), (2,1), (3,0), (4,-1)
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For K = {(x, y) | x - y = 5}, what are the output pairs when the domain of x is 0, 2, 4?
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Use the graph of the function to evaluate f(2).
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Study Notes
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.
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Description
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.