Select all the transformations of f(x) = x2 that combine to result in the graph of function g below. A parabola with vertex negative 1 comma negative 2 that opens downward. The graph passes through the points negative 3 comma negative 3 and 1 comma negative 3.

Group of answer choices

vertical stretch by a factor of 2

translation of 1 unit right

translation of 2 units up

translation of 1 unit left

reflection across the x-axis

horizontal stretch by a factor of 2

translation of 2 units down

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)