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Which best describes the asymptote of an exponential function of the form F(x) = b^x?

AVertical asymptote at x = 0
BVertical asymptote at x = 1
CHorizontal asymptote at y = 0
DHorizontal asymptote at y = 1

Verified Answer :

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.

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