Describe the end behavior of the function below f(x)=4(2)^(-x)-3

Step-by-step explanation:

f(x)=4(2)^(-x) is a decreasing exponential function.  We know that because of the negative exponent, -x.  As x increases, f(x) decreases towards the x-axis, but never touches that axis.

If, however, we have f(x)=4(2)^(-x) -  3, the graph of this function shows the result of translating the entire graph down 3 units.  Now, as x increases, f(x) decreases towards the horizontal line y = -3, but never touches that line.