Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
[tex]\boxed{f(x)=\frac{2x(x+3)}{(x-2)(x-3)}}\\\\check:\\vertical\ asymptotes:(x-2)(x-3)\neq0\to x\neq2\ and\ x\neq3\\\boxed{x=2\ and\ x=3}\\\\x-intercepts:f(x)=0\iff\frac{2x(x+3)}{(x-2)(x-3)}=0\iff2x(x+3)=0\\\iff 2x=0\ or\ x+3=0\iff \boxed{x=0\ or\ x=-3}\\\\horizontal\ asymptote:\\\lim\limits_{x\to\pm\infty}\frac{2x(x+3)}{(x-2)(x-3)}=\lim\limits_{x\to\pm\infty}\frac{2x^2+6x}{x^2-5x+6}=\lim\limits_{x\to\pm\infty}\frac{x^2(2+\frac{6}{x})}{x^2(1-\frac{5}{x}+\frac{6}{x^2})}=\frac{2}{1}=\fbox2[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
