Short Answer 
The exponential function, defined as y = b^x, exhibits growth or decay depending on the base b, with b > 0 indicating growth and b < 0 indicating decay. These functions have a distinct curve shape, consistently either rising or falling without reversing direction, influenced significantly by the value of b.
Step 1: Understanding the Exponential Function
The exponential function is defined by the formula y = b^x, where b represents the base and must be greater than zero for growth, while it will be less than zero for decay. The variable x acts as the exponent. This means that depending on the value of b:
- b > 0: The function is exponentially growing.
- b < 0: The function is exponentially decaying.
Step 2: Behavior of Exponential Functions
Exponential functions have a characteristic shape where the graph curves upwards for increasing functions and approaches zero for decreasing functions. For example, the graph of y = 2^x illustrates an exponential growth pattern. It’s essential to note that regardless of whether the function is increasing or decreasing, exponential functions maintain a monotonic behavior, meaning they do not reverse direction.
Step 3: Analyzing Different Exponential Functions
To illustrate the impact of different values of b on the function, consider y = -3^x. This example shows an exponential decay. Throughout these functions, the base b heavily influences whether the graph continuously rises or falls. For further details on these concepts, additional resources are available through the provided link.