Question

Why do basic exponential functions always have a horizontal asymptote at y = 0?

Answer 1

Answer:

As x-approaches infinity, we get a rational function whose denominator becomes bigger and bigger while the numerator is constant

Step-by-step explanation:

The basic exponential functions are of the form:

$y = {b}^{ x}$

where b is a constant.

Horizontal is the horizontal line the graph of a function approaches when as x-values approaches infinity.

For exponential growth functions, as x-approaches negative infinity the function approaches zero, i.e y=0.

For exponential decay functions as x-approaches positive infinity the function approaches zero.

The reason is that, in each case we get a rational expression whose denominator grows bigger and bigger, while the numerator remains constant.