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 need to look for two main characteristics:
1. The vertical line test: If every vertical line drawn on the graph intersects the curve at most once, then the graph represents a function. This means that for each value of x on the x-axis, there is only one corresponding value of y on the y-axis.
2. The horizontal line test: If no horizontal line intersects the graph in more than one point, then the graph represents a function. This means that for each value of y on the y-axis, there is only one corresponding value of x on the x-axis.
By examining these two tests, we can determine if the graph shown represents a function or not. If any vertical line intersects the graph at more than one point, or if any horizontal line intersects the graph at more than one point, then the graph does not represent a function.