Question

An exponential growth function has an asymptote of y = –3. Which might have occurred in the original function to permit the range to include negative numbers?

Answer 1

Answer:

A whole number constant, which is 3, could have been subtracted from the original exponential expression.

Step-by-step explanation:

The original exponential function is expressed as

$f(x)= A^{x}$

The graph of this function has a horizontal asymptote at y = 0, because $A^{x}$ > 0 for all x.

The range of the original function changed to y=-3. Therefore, the graph of this function is shifted down. The shift can be written down as:

$f(x)=A^{x} -3$

This means that the whole number 3 has been subtracted from the original exponential expression.