Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the function as $y=\frac{(x-7)(x+7)}{(x-2)(x+7)}=\frac{x-7}{x-2}=1-\frac{5}{x-2}, x\ne-7$, we can identify a hole at $x=-7$, a vertical asymptote at $x=2$ and a horizontal asymptote at $y=1$. The domain can be found to be all real numbers except $x\ne-7,2$.
Step 2. Take derivatives to get $y'=\frac{5}{(x-2)^2}$ and $y''=-\frac{10}{(x-2)^3}$. Since $y'\gt0$ for all values in the domain, the function will be increasing for all $x$. For $y''\gt0$ the function will be concave up when $x\lt2$,, and for $y''\lt0$ the function will be concave down when $x\gt2$. There is no inflection point as the function is not defined at $x=2$.
Step 3. The y-intercepts can be found by letting $x=0$ to get $y=7/2$, and the x-intercepts can be found by letting $y=0$ to get $x=7$
Step 4. Based on the above results, we can graph the function as shown in the figure.
