9.4 THE SIGMOID ACTIVATION FUNCTION
A common activation function is the sigmoid function
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c9-disp-0007.png)
Why use the sigmoid function? Because it combines nearly linear behavior, curvilinear behavior, and nearly constant behavior, depending on the value of the input. Figure 9.4 shows the graph of the sigmoid function for −5 < x < 5. Through much of the center of the domain of the input x (e.g. –1 < x < 1), the behavior of f(x) is nearly linear. As the input moves away from the center, f(x) becomes curvilinear. By the time the input reaches extreme values, f(x) becomes nearly constant.
![Image described by caption and surrounding text.](https://static.packt-cdn.com/products/9781119526810/graphics/images/c09f004.gif)
Figure 9.4 Graph of the sigmoid function y = f(x) = 1/(1 + e–x).
Moderate increments in the value of x produce varying increments in the value of f(x), depending on the location of x. Near the center, moderate increments in the value of x produce moderate increments in the value of f(x); however...