Please answer the following questions about the function

Instructions: If you are asked to find [math]- or [math]-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 [math], where it is increasing and decreasing, and its local extrema.
Critical numbers [math]
Increasing on the interval
Decreasing on the interval
Local maxima [math]
Local minima [math]

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

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

(d) The function [math] is because for all [math] in the domain of [math], and therefore its graph is symmetric about the

(e) Sketch a graph of the function [math] without having a graphing calculator do it for you. Plot the [math]-intercept and the [math]-intercepts, if they are known. Draw dashed lines for horizontal and vertical asymptotes. Plot the points where [math] 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 [math]. 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.