Why does this plot correspond to this function?

1. Which correspondence represent a function why?
2. How do you explain why a graph is a function?
3. Does this graph represent a function why or why not?
4. What does the derivative of a function correspond to?

Which correspondence represent a function why?

A function is a correspondence between two sets where each element in the first set, called the domain, corresponds to exactly one element in the second set, called the range. Note that the definition of a function is more restrictive than the definition of a relation.

How do you explain why a graph is a function?

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

Does this graph represent a function why or why not?

If a vertical line drawn anywhere on the graph of a relation only intersects the graph at one point, then that graph represents a function. If a vertical line can intersect the graph at two or more points, then the graph does not represent a function.

What does the derivative of a function correspond to?

As we have seen, the derivative of a function at a given point gives us the rate of change or slope of the tangent line to the function at that point. If we differentiate a position function at a given time, we obtain the velocity at that time.