Final answer:
To determine if a set of points represents a function, each input or x-coordinate must have only one output or y-coordinate. This is known as the vertical line test.
Correct option is B) E, G
Step-by-step explanation:
To determine which set of points represents a function, you need to understand the definition of a function in mathematics. A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
In mathematical terms, for any x-coordinate in the set, there should only be one unique y-coordinate. This is often referred to as the 'vertical line test'. If you can draw a vertical line that intersects the graph at more than one point, then the set of points does not represent a function.
Let's analyze the given sets of points:
- Option A) E, H, G - If there are multiple points with the same x-coordinate (meaning E, H, and G all have different y-coordinates), this does not pass the vertical line test and is not a function.
- Option B) E, G - If E and G each have a unique x-coordinate, this set can represent a function.
- Option C) E, H - Like option B, if E and H each have a unique x-coordinate, this set can represent a function.
- Option D) H, G - If H and G each have a unique x-coordinate, this set can also represent a function.
Without specific coordinates, we can't definitively say which set is a function, but options B, C, and D are all potentially correct if they adhere to the vertical line test. For example, if set E represents (2,3), set H represents (4,5), and set G represents (6,7), then options B, C, and D would all be functions since each x-coordinate has a different y-coordinate. However, since we do not have the actual coordinates, it is impossible to choose the correct answer from the given options without more information.