If f(x) = x^2, which of the following describes the graph of f(x) - 5?
a.) the graph of f(x) - 5 is a vertical shift of f(x) = x^2 five units up.
b.) the graph of f(x) - 5 is a horizontal shift of f(x) = x^2 five units to the left.
c.) the graph of f(x) - 5 is a vertical shift of f(x) = x^2 five units down.
d.) the graph of f(x) - 5 is a horizontal shift of f(x) = x^2 five units to the right.

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.