# Impossible Graphs

Shodor > Interactivate > Discussions > Impossible Graphs

 Student: What does it mean for a graph to be impossible? After all, it is just an abstract picture. Mentor: A graph is an abstract picture which represents something in reality so a graph cannot represent something in reality which cannot exist or happen. For example the following graph would be impossible because it shows negative mass: Student 1: I can make another graph that would be impossible for many situations in the real world. If there is a graph of distance vs. time, it can't have gaps, because distance can only change continuously with time. In this graph, the distance changes instantaneously by too large an amount: Mentor: That's true! We can distinguish between continuous graph which you could draw without ever lifting your pencil, and a discontinuous graph which may have gaps, as long as it has one and only one y-value for each x-value. Can you tell me why this graph is impossible? Student: Because the graph shows time moving backwards.. Mentor: Exactly. As you can see, to decide whether each graph is possible or not, we mostly need common sense. Student: It also helps to know the laws! Mentor: That's true. Knowing the laws could never hurt.