Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the function as
$f(x)=\frac{(2x-1)(x-2)}{(x+2)(x-2)}=\frac{2x-1}{x+2}$
with a hole at
$(2,\frac{3}{4})$
Step 2. We have
$f(-x)=\frac{-2x-1}{-x+2}=\frac{2x+1}{x-2}$
Thus, there is no symmetry.
Step 3. We can find a vertical asymptote as $x=-2$
Step 4. We can find a horizontal asymptote as $y=2$
Step 5. Find the x-intercepts as $x=\frac{1}{2}$
Step 6. Find the y-intercept as $f(0)=-\frac{1}{2}$
Step 7. Using test points and the information above, we can graph the function as shown.
