1. **State the problem:** We are given the function $f(x) = -5^x$ and asked to find its vertical and horizontal asymptotes. 2. **Recall the definitions:** - A **vertical asymptote** occurs where the function approaches infinity or negative infinity as $x$ approaches a certain value. - A **horizontal asymptote** is a horizontal line that the graph approaches as $x$ goes to $+\infty$ or $-\infty$. 3. **Analyze the function:** - The function is $f(x) = -5^x$, which is an exponential function with base 5 and a negative sign. - Exponential functions of the form $a^x$ with $a>1$ have no vertical asymptotes because they are defined for all real $x$. 4. **Vertical asymptotes:** - Since $f(x)$ is defined for all real $x$, there are no vertical asymptotes. 5. **Horizontal asymptotes:** - As $x \to +\infty$, $5^x \to +\infty$, so $f(x) = -5^x \to -\infty$. - As $x \to -\infty$, $5^x \to 0^+$, so $f(x) = -5^x \to 0^-$. - Therefore, the horizontal asymptote is the line $y=0$. **Final answer:** - Vertical asymptotes: None - Horizontal asymptote: $y=0$