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.

4. Quadratic Functions

Quadratic functions are mathematical models that show how the value of x changes at a constant rate while increasing in slope. An example would be x^2. In this case, we would have a graph that shows us that the values of x increase by four each time. The graph shows us that the slope of the line increases by two each time as well.

5. Cubic Functions

Cubic functions are mathematical models that depict how the value of x varies at a constant rate while decreasing in slope. An example is x^3.