Question

1. 0.75 / 1.25 points details my notes previous answers the exponential function ( f(x)=left(\frac{1}{8}

ight)^{x} ) has the horizontal asymptote ( y = 0 ). this means that as ( x
ightarrow infty ), we have ( left(\frac{1}{8}
ight)^{x}
ightarrow ) enter an exact number.

Explanation:

Step1: Analyze the exponential function

For an exponential function \(y = a^x\) where \(0 < a<1\), as \(x
ightarrow\infty\), \(y
ightarrow0\). Here \(a=\frac{1}{8}\) (since \(0<\frac{1}{8}<1\)).

Step2: Evaluate the limit

We want to find \(\lim_{x
ightarrow\infty}(\frac{1}{8})^x\). Using the property of exponential functions, if \(0 < b<1\), then \(\lim_{x
ightarrow\infty}b^x = 0\). So \(\lim_{x
ightarrow\infty}(\frac{1}{8})^x=0\)

Answer:

\(0\)