(Solved): (10) Explain why the graph shown below is the graph of \( f(x)=\frac{x-2}{x^{2}-4} \). (Hint: you ...

(10) Explain why the graph shown below is the graph of \( f(x)=\frac{x-2}{x^{2}-4} \). (Hint: you may use horizontal asymptote, vertical asymptote, domain, intercepts, hole, end behaviour, ... to justify) (11) Consider the function \( r(x)=\frac{x\left(x^{2}-16\right)}{(x+3)\left(7 x^{2}+1\right)} \). Find all asymptotes, intercepts, and holes (if any). Show all your work. (12) A large mixing tank currently contains 100 gallons of water, into which 5 pounds of sugar have been mixed. A tap will open pouring 10 gallons per minute of water into the tank at the same time sugar is poured into the tank at a rate of 1 pound per minute. Find the concentration (pounds per gallon) of sugar in the tank after \( t \) minutes.