Algebra-1

Let’s break down the end behavior of this function in detail.

Consider a typical exponential function, such as    where a > 1. The behavior of this function as x approaches negative and positive infinity can be analyzed as follows:

1. As :

Behavior: As x becomes very large in the negative direction (i.e., approaches negative infinity), the exponential function behaves in a specific way. For instance, if we consider where a > 1:

For very negative values of x, approaches 0 (but never actually reaches 0 ).

This is because raising a number greater than 1 to a large negative exponent results in a very small positive number.

 Conclusion: Therefore, we can say:  as .

2. As