1. The problem is to analyze and graph the function $y=\left(\frac{1}{10}\right)^x$. 2. The formula for exponential functions is $y=a^x$ where $a>0$ and $a\neq1$. 3. Important rules: - If $01$, the function is increasing. - The graph passes through the point $(0,1)$ because $a^0=1$. - The $x$-axis ($y=0$) is a horizontal asymptote. 4. For $y=\left(\frac{1}{10}\right)^x$, since $\frac{1}{10}=0.1$ which is between 0 and 1, the function is decreasing. 5. Evaluate some points: - At $x=0$: $y=\left(\frac{1}{10}\right)^0=1$ - At $x=1$: $y=\frac{1}{10}=0.1$ - At $x=-1$: $y=\left(\frac{1}{10}\right)^{-1}=10$ 6. The graph passes through $(0,1)$, $(1,0.1)$, and $(-1,10)$ and approaches $y=0$ as $x\to\infty$. 7. The final answer is the function $y=\left(\frac{1}{10}\right)^x$ which is a decreasing exponential function with horizontal asymptote $y=0$ and passes through $(0,1)$.