Please answer the following questions about the function

Instructions: If you are asked to find - or
-values, enter either a number, a list of numbers separated by
commas, or None if there aren't any solutions.
Use interval notation if you are asked to find an
interval or union of intervals, and enter { } if the interval
is empty.

(a) Find the critical numbers of , where it is increasing and
decreasing, and its local extrema.
Critical numbers
Increasing on the interval
Decreasing on the interval
Local maxima
Local minima

(b) Find where is concave up, concave down, and has inflection points.
Concave up on the interval
Concave down on the interval
Inflection points

(c) Find any horizontal and vertical asymptotes of .
Horizontal asymptotes
Vertical asymptotes

(e) Sketch a graph of the function without having a graphing
calculator do it for you. Plot the -intercept and the
-intercepts, if they are known. Draw dashed lines for horizontal
and vertical asymptotes. Plot the points where has local
maxima, local minima, and inflection points. Use what you know from
parts (a) and (b) to sketch the remaining parts of the graph of . Use any symmetry from part (d) to your advantage. Sketching
graphs is an important skill that takes practice, and you may be asked
to do it on quizzes or exams.