Question

Which best describes the asymptote of an exponential function of the form F(x) = b^x?
A. Vertical asymptote at x = 0
B. Vertical asymptote at x = 1
C. Horizontal asymptote at y = 0
D. Horizontal asymptote at y = 1

Answer 1

Answer:

C. Horizontal asymptote at $y=0$.

Step-by-step explanation:

We are asked to choose the option that best describes the asymptote of an exponential function of the form $F(x)=b^x$.

We know that exponential functions always have horizontal asymptotes. The horizontal asymptote for an exponential function in form $f(x)=A(b)^x+c$  is at $y=c$.

Upon looking at our given function we can see that value of 'c' is 0, therefore, our given function will have a horizontal asymptote at $y=0$ and option C is the correct choice.

Answer 2

Using the asymptotes definition, it is found that the statement that best describes the asymptote of an exponential function of the form F(x) = b^x is:

C. Horizontal asymptote at y = 0.

What are the asymptotes of a function f(x)?

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, we have the exponential function given by:

$F(X) = b^x$

It has no restrictions in the domain, hence there are no vertical asymptotes.

For the horizontal asymptotes, we have that:

$y = \lim_{x \rightarrow \pm \infty} f(x)$

Hence:

$y = \lim_{x \rightarrow -\infty} f(x) = b^{-\infty} = \frac{1}{b^{\infty}} = 0$

$y = \lim_{x \rightarrow \infty} f(x) = b^{\infty} = \infty$

Hence, statement C is correct.

You can learn more about asymptotes at https://brainly.com/question/16948935