Problem

Graph the equation on paper, and then choose the correct graph on the right. \[ y=\left(\frac{1}{4}\right)^{x} \] Choose the correct graph.

Solution

Step 1 :The question is asking to graph the equation \(y=(1/4)^x\). This is an exponential function with base 1/4.

Step 2 :The graph of an exponential function with base less than 1 is a decreasing function. It starts from a high value (when x is negative) and decreases towards 0 as x increases.

Step 3 :To generate the graph, we can use a range of x values and compute the corresponding y values using the given equation. Then we plot these points to get the graph.

Step 4 :The graph generated shows a decreasing function as expected. The function starts from a high value when x is negative and decreases towards 0 as x increases. This is consistent with the properties of an exponential function with base less than 1.

Step 5 :\(\boxed{\text{Final Answer: The graph of the function } y=\left(\frac{1}{4}\right)^{x} \text{ is a decreasing function that starts from a high value when x is negative and decreases towards 0 as x increases.}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/BiD2swreGE/

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