Determine whether the function is continuous on the given interval.
Yes. f is only discontinuous when x = -1, which is not in the interval (-3,-2), therefore f is continuous on (-3,-2).
Yes, g is continuous on this interval. g is discontinuous when x = 3, but this value is not in the interval (0,3).
Yes, h is continuous on this interval. The only value we need to worry about is x = 4, but h is continuous there.
No. m is discontinuous at 3 because m(3) = 6 but .
Yes. The denominator factors as (x +2)(x + 1) so the function is undefined at x = -2 and x = -1. These are the only points of discontinuity, but neither is in the interval (1, 3).
Determine whether the function f is continuous on each interval.
Since we're asked about the same function on so many intervals, first we'll figure out all the values at which f is discontinuous.
The right-hand limit is
Since the one-sided limits disagree, does not exist, and f is discontinuous at x = 0.
To summarize, f is discontinuous at x = 0, x = 1, and x = 2.Now we can answer the real questions.
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