What is the best way to determine whether a graph is a function or not?
Answer (1)
Answer:The best way to determine whether a graph represents a function is to use the Vertical Line Test. Here's how it works: 1. Draw a vertical line: Imagine drawing a vertical line anywhere on the graph.2. Check for intersections: Observe how many times the vertical line intersects the graph.3. Apply the rule:- If the vertical line intersects the graph at only one point for every possible vertical line, then the graph represents a function.- If the vertical line intersects the graph at more than one point for even one possible vertical line, then the graph does not represent a function. Why does this work? - A function, by definition, assigns each input (x-value) to exactly one output (y-value).- The Vertical Line Test checks this: If a vertical line intersects the graph at more than one point, it means that for that particular x-value, there are multiple y-values. This violates the definition of a function. Example: - Function: A straight line (not vertical) or a parabola. No matter where you draw a vertical line, it will only intersect the graph once.- Not a Function: A circle or a vertical line. You can easily draw a vertical line that intersects the graph more than once.
