Questions: Graph the exponential function. g(x)=(1/4) 2^(-x) Choose the letter that corresponds to the correct graph. A C D

Transcript text: Graph the exponential function. \[ g(x)=\left(\frac{1}{4}\right) 2^{-x} \] Choose the letter that corresponds to the correct graph. A C D

Solution

Solution Steps

Step 1: Identify the Exponential Function

The given exponential function is \( g(x) = \left(\frac{1}{4}\right)^{2-x} \).

Step 2: Simplify the Exponential Function

Rewrite the function to make it easier to graph: \[ g(x) = \left(\frac{1}{4}\right)^{2-x} = \left(\frac{1}{4}\right)^2 \cdot \left(\frac{1}{4}\right)^{-x} = \frac{1}{16} \cdot 4^x \]

Step 3: Determine the General Shape of the Graph

The function \( g(x) = \frac{1}{16} \cdot 4^x \) is an exponential growth function because the base \( 4 \) is greater than 1. The graph will increase rapidly as \( x \) increases.