Hi I was wondering if I could get some help with this question please 26POINTS!! PLEASE HELP
given the parent function f(x)=√x and a new function g(x)=√x+6+3. Select from the drop-down menus to correctly describe the changes on the graph from f(x) to g(x).

The graph will shift 6 unitand 3 units.
choices:up up
down down
left left
right right

Factor -8x3-2x2-12x-3 by grouping what is the resulting expression?

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the curves about the given axis.y = 7ex, y = 7e^-x, x = 1; about the y-axis

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.