Final answer:
The relation (1,-2), (2,1), (3,6), (4,13), (5,22) is a function because each x-value is paired with a unique y-value, and it passes the vertical line test. There are no repeating x-values, ensuring each input has only one corresponding output. The correct answer is A.
Step-by-step explanation:
The question asks if the relation (1,-2), (2,1), (3,6), (4,13), (5,22) is a function. We can determine this by checking if each input (x-value) maps to exactly one output (y-value). If an x-value is paired with more than one y-value, it is not a function. Looking at the given set of points, we can see that each x-value is distinct and is paired with only one y-value. Therefore, this relation is a function, making option A correct because each input has a unique output.
The concept of a function in mathematics is critical to understanding and representing the dependence of y on x. When represented graphically, such as in the provided example with different points, a function will pass the vertical line test. This means that a vertical line drawn at any point along the x-axis will intersect the graph at no more than one point. Since the given relation shows no repeated x-values, it would pass the vertical line test, providing further evidence that it is indeed a function.
In the context of linear equations, we often look at the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept. For a set of points or a relation to represent a linear equation specifically, it must form a straight line when plotted on a graph. The points listed in the question do not necessarily indicate a linear function, but the absence of a distinct pattern does not disprove it being a function at all. Therefore, option D is incorrect. The question focuses on the definition of a function rather than the specific type of function or its graphical representation.