The Graphs of Exponential Functions

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If the number on the x is a positive integer, you divide the subsequent number on it’s y axis in half. This would make the number on the y axis a fraction, turning smaller and smaller every time. If the number on x axis is a negative integer, it’s y axis counterpart would be a natural number (at least according to our data). The number subsequent to the last one would be doubled, and that would stay the pattern to finding the next y axis number on this exponential graph. The numbers on this graph are always positive, however it may not look like it. All positive integers graphed on the x axis have a fraction as their y axis counterpart, so every number above zero would be between 0 and 1. Suddenly, as we jump from positive to negative x axis integers, the numbers skyrocket to enormously large positive numbers. That would represent the sudden rise from a horizontal asymptote to numbers that would go off the graph. A group with a similar pattern to ours would be group 1. Their equation was y=x^2, which would give them answers virtually the opposite of ours, because y=2^-x is the exact opposite of the other equation. When they would happen to have 1024 on the y axis, we would have 1/1024. Here is a picture of their exponential graph:

 This project allowed me to understand what the relationships between negative and positive exponents were!