Question

the exponential function f(x)=(1/4)^x has the slant asymptote y = enter an exact number. this means that as x→∞, we have (1/4)^x→

Explanation:

Step1: Recall exponential - function property

For an exponential function of the form \(y = a^x\), when \(0\lt a\lt1\), as \(x\to\infty\), \(y\to0\). Here \(a=\frac{1}{4}\) which is between \(0\) and \(1\).

Step2: Determine the horizontal asymptote

The horizontal asymptote of the function \(f(x)=(\frac{1}{4})^x\) is \(y = 0\) because as \(x\) approaches infinity, the value of \((\frac{1}{4})^x\) approaches \(0\).

Answer:

0