Question

find the graph of the following exponential function. y = \frac{1}{2} \cdot \left(\frac{1}{4}\
ight)^x

Explanation:

Step1: Analyze the form of the exponential function

The general form of an exponential function is \(y = a\cdot b^{x}\). Here \(a=\frac{1}{2}\) and \(b = \frac{1}{4}\). Since \(0 < b<1\), the function is a decreasing exponential function.

Step2: Find the y - intercept

When \(x = 0\), \(y=\frac{1}{2}\cdot(\frac{1}{4})^{0}\). According to the rule \(a^{0}=1(a
eq0)\), we have \(y=\frac{1}{2}\times1=\frac{1}{2}\).

Answer:

The left - hand graph (the decreasing one) is the graph of the function \(y=\frac{1}{2}\cdot(\frac{1}{4})^{x}\)