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Problem : Is the following function continuous: f (x) = 3x2 + 2? If not, what type of discontinuity exists?

Yes, it is continuous -- it is a polynomial.

Problem : Is the following function continuous: f (x) = ? If not, what type of discontinuity exists?

No, it is discontinuous. There exists an infinite discontinuity at x = 0.

Problem : Is the following function continuous: f (x) = tan(x)? If not, what type of discontinuity exists?

No, it is discontinuous. An infinite discontinuity exists at the points x = + nΠ, where n is any integer.

Problem : Is the following function continuous: f (x) = ? If not, what type of discontinuity exists?

No, it is discontinuous. At x = 0, a point discontinuity exists.

Problem : Is the following function continuous: f (x) = x)? If not, what type of discontinuity exists?

Yes, it is continuous (for all x > 0, of course--this is the domain of the function).
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