# Examples of Mathematical Plots

1. Exponential Growth

An exponential function is a mathematical model where the value of x increases at a constant rate over time. An example of an exponential function would be 1 + 2x. In this case, if we were to graph the function, we could see that the value of x increases by two each time. If we were to graph the equation above, we would get a graph that shows that the value of x doubles after every period of time. The graph also shows that the value of y increases at a constant rate.

2. Logarithmic Function

A logarithmic function is a mathematical model that describes how the value of x decreases at a constant rate over a given amount of time. An example of a logarithmic function would be -log(x). In this case, if the value of x was 0.01, then the value of -log(0.01) would be approximately 4.9. If we were to plot this function, the graph would show us that the value of x decreases by half each time. The graph also tells us that the value of y decreases at a constant rate.

3. Linear Functions

Linear functions are mathematical models that describe how the value of x increases or decreases at a constant rate without any change in slope. An example of a linear function would be x=5. In this case, the value of x does not change. However, if we were to draw this function, we would end up with the graph in which the value x stays the same throughout the entire graph. The graph would also show us that the value y increases at a constant pace.