Questions: Graph the equation on paper, and then choose the correct graph on the right. y=(1/3)^x Choose the correct graph. A. C. B. D.

Solution Steps

The given equation is \(y = (\frac{1}{3})^x\). This is an exponential function with a base of \(\frac{1}{3}\). Since the base is between 0 and 1, the function represents exponential decay. This means the graph will decrease as \(x\) increases. It will also have a horizontal asymptote at \(y = 0\).

Let's find a few points to help identify the correct graph.

• When \(x = 0\), \(y = (\frac{1}{3})^0 = 1\).
• When \(x = 1\), \(y = (\frac{1}{3})^1 = \frac{1}{3}\).
• When \(x = 2\), \(y = (\frac{1}{3})^2 = \frac{1}{9}\).
• When \(x = -1\), \(y = (\frac{1}{3})^{-1} = 3\).
• When \(x = -2\), \(y = (\frac{1}{3})^{-2} = 9\).

We are looking for a graph that passes through the points \((0, 1)\), \((1, \frac{1}{3})\), \((2, \frac{1}{9})\), \((-1, 3)\), and \((-2, 9)\) and shows exponential decay. Graph A matches this description.

Final Answer