How can we determine from a graph if a function is shown or not?
To determine if a function is shown on a graph, we typically look for two key properties: the vertical line test and the existence of multiple points with the same x-coordinate.
1. Vertical Line Test: A graph represents a function if every vertical line intersects the graph at most once. In other words, if we can draw a vertical line that passes through any point on the graph and intersects the graph in only one place, then the graph represents a function. If, however, there exists a vertical line that intersects the graph at multiple points, then the graph does not represent a function.
2. Multiple points with the same x-coordinate: A graph does not represent a function if there are any points in the graph that have the same x-coordinate but different y-coordinates (i.e., different vertical positions). This violates the definition of a function, which states that for every input (x-value), there should be exactly one output (y-value).
By carefully examining the graph and applying these two criteria, we can determine if a function is shown or not.