1. **State the problem:** We are given the function $y = -\left(\frac{1}{3}\right)^x$ and want to understand its behavior. 2. **Formula and rules:** The function is an exponential function of the form $y = -a^x$ where $a = \frac{1}{3}$, which is between 0 and 1. This means the function $a^x$ is a decreasing exponential. 3. **Analyze the function:** - Since $a = \frac{1}{3}$, $a^x$ decreases as $x$ increases. - The negative sign in front flips the graph over the x-axis. 4. **Evaluate key points:** - At $x=0$, $y = -\left(\frac{1}{3}\right)^0 = -1$. - At $x=1$, $y = -\frac{1}{3} \approx -0.333$. - At $x=-1$, $y = -3$ because $\left(\frac{1}{3}\right)^{-1} = 3$. 5. **Behavior:** - As $x \to \infty$, $\left(\frac{1}{3}\right)^x \to 0$, so $y \to 0$ from below. - As $x \to -\infty$, $\left(\frac{1}{3}\right)^x \to \infty$, so $y \to -\infty$. 6. **Summary:** The graph is a decreasing exponential flipped over the x-axis, passing through $(0,-1)$, approaching 0 from below as $x$ increases, and going to negative infinity as $x$ decreases. Final answer: The function is $y = -\left(\frac{1}{3}\right)^x$ with the described behavior.