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?
A whole number constant could have been added to the exponential expression.
A whole number constant could have been subtracted from the exponential expression.
A whole number constant could have been added to the exponent.
A whole number constant could have been subtracted from the exponent.

Answer 1

Answer: C. A whole number constant could have been added to the exponent.

Step-by-step explanation: On Edge!

Answer 2

The right choice is: A whole number constant could have been subtracted from the exponential expression.

Let be an exponential function of the form $y = A\cdot e^{B\cdot x}$, where $A$ and $B$ are real numbers. A horizontal asymptote exists when $e^{B\cdot x} \to 0$, which occurs for $B\cdot x \to - \infty$.

For this function, the horizontal asymptote is represented by $y = 0$ and to change the value of the asymptote we must add the parent function by another real number ($C$), that is to say:

$y = A\cdot e^{B\cdot x} + C$ (1)

In this case, we must use $C = -3$ to obtain an horizontal asymptote of -3. Thus, the right choice is: A whole number constant could have been subtracted from the exponential expression.

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