)a function f is defined as f(x) = 3*2^x

describe the end behavior of f, please describe in detail how you got the answer and explain your abbreviations.

F(x) = 3*2^x.

F(-2) = 3 * 2^-2 = 0.75.

F(-1) = 3 * 2^-1 = 1.50.

F(0) = 3 * 2^0 = 3.0.

F(1) = 3 * 2^1 = 6.0

So when x is increased by 1, F(x) doubles. This is normal behavior for
base 2 numerals.

To describe the end behavior of the function f(x) = 3 * 2^x, we can analyze what happens to the function as x approaches positive and negative infinity.

First, let's examine the term 2^x. As x approaches positive infinity, the exponent x becomes larger and larger. When x is positive, 2^x also becomes larger, approaching infinity. Similarly, as x approaches negative infinity, the exponent x becomes more negative. For negative exponents, 2^x approaches 0 as x becomes more negative, getting closer to the x-axis.

Now, multiplying 3 by 2^x in the given function f(x) = 3 * 2^x implies that the function f(x) will also follow the same behavior. So, here's the detailed analysis:

1. As x approaches positive infinity, 2^x becomes larger and larger, approaching infinity. As a result, the factor 3 * 2^x will also approach infinity, meaning that f(x) increases without bound.

2. As x approaches negative infinity, 2^x becomes smaller and smaller, approaching 0. Multiplying by 3 won't change this behavior. Therefore, the factor 3 * 2^x will approach 0, indicating that f(x) approaches 0 as x approaches negative infinity.

To summarize, the end behavior of the function f(x) = 3 * 2^x is as follows:
- As x approaches positive infinity, f(x) increases without bound (towards positive infinity).
- As x approaches negative infinity, f(x) approaches 0.

Abbreviations used:
- Infinity (∞): A concept representing an extremely large value, without any finite bound.
- Exponent (x): The power to which a base (in this case, 2) is raised.
- End behavior: Describes how the function behaves as x approaches positive or negative infinity.