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