Below is a list of features of a graph of a function. {{CMD_12}} {{CMD_13}} Find the points {{MATH_14}} where {{MATH_15}} goes to infinity as {{MATH_16}} goes to {{MATH_17}} (from the right, left, or both). These are the points where {{MATH_18}} has a vertical asymptote. {{CMD_19}} Find the critical points (the points where {{MATH_20}} or {{MATH_21}} is undefined). {{CMD_22}} Identify inflection points and concavity. {{CMD_23}} Determine an interval that shows all relevant behavior. {{CMD_24}} Find the {{MATH_25}}-intercept, this is the point {{MATH_26}}. Place this point on your graph. {{CMD_27}} Find the candidates for inflection points, the points where {{MATH_28}} or {{MATH_29}} is undefined. {{CMD_30}} If possible, find the {{MATH_31}}-intercepts, the points where {{MATH_32}}. Place these points on your graph. {{CMD_33}} Compute {{MATH_34}} and {{MATH_35}}. {{CMD_36}} Analyze end behavior: as {{MATH_37}}, what happens to the graph of {{MATH_38}}? Does it have horizontal asymptotes, increase or decrease without bound, or have some other kind of behavior? {{CMD_39}} {{CMD_40}} Use either the first or second derivative test to identify local extrema and/or find the intervals where your function is increasing/decreasing. In what order should we take these steps? For example, one must compute {{MATH_41}} before computing {{MATH_42}}. Also, one must compute {{MATH_43}} before finding the critical points. There is more than one correct answer. {{CMD_44}} Here is one possible answer to this question. Compare it with yours! {{CMD_45}} {{CMD_46}} Find the {{MATH_47}}-intercept, this is the point {{MATH_48}}. Place this point on your graph. {{CMD_49}} Find any vertical asymptotes, these are points {{MATH_50}} where {{MATH_51}} goes to infinity as {{MATH_52}} goes to {{MATH_53}} (from the right, left, or both). {{CMD_54}} If possible, find the {{MATH_55}}-intercepts, the points where {{MATH_56}}. Place these points on your graph. {{CMD_57}} Analyze end behavior: as {{MATH_58}}, what happens to the graph of {{MATH_59}}? Does it have horizontal asymptotes, increase or decrease without bound, or have some other kind of behavior? {{CMD_60}} Compute {{MATH_61}} and {{MATH_62}}. {{CMD_63}} Find the critical points (the points where {{MATH_64}} or {{MATH_65}} is undefined). {{CMD_66}} Use either the first or second derivative test to identify local extrema and/or find the intervals where your function is increasing/decreasing. {{CMD_67}} Find the candidates for inflection points, the points where {{MATH_68}} or {{MATH_69}} is undefined. {{CMD_70}} Identify inflection points and concavity. {{CMD_71}} Determine an interval that shows all relevant behavior {{CMD_72}} {{CMD_73}} {{CMD_74}}