Basic Mathematics20795 marksNumerical: horizontal and vertical asymptotesHorizontal asymptotes
Define horizontal and vertical asymptotes. Find the appropriate asymptotes to the function: f(x) = x - sqrtx2 + 16. [2+3]
Define horizontal and vertical asymptotes. Find the appropriate asymptotes to the function: $f(x) = x - \sqrt{x^2 + 16}$. [2+3]
- Function: $f(x) = x - \sqrt{x^2 + 16}$ - Domain check: $x^2 + 16 0$ for all real $x$, so domain is all of $\mathbb{R}$. --- (a) Definitions Horizontal Asymptote: A line $y = L$ is a horizontal asymptote of $y = f(x)$ if $$\lim{x \to +\infty} f(x) = L \quad \text{or} \quad \lim{x \to -\infty} f(...