Locate where the following function is discontinuous, and classify each type of discontinuity.
Hint
Factor first.
Answer
x = 3, hole ; x = -3, vertical asymptote
If the function is discontinuous, it will fail one of the three requirements for continuity.
The function has no discontinuities.
If you're unsure, plug in some values or graph it.
x = -4, jump
Is the following function continuous at the given x value? If not, is it a hole, a jump, or a vertical asymptote?
f(x) = tan (x), at
Tangent has these on a regular basis.
Not continuous, vertical asymptote.
, at x = -1
Factor, then check to see if any action is happening at x = -1.
Not continuous, hole.
, at x = 0
We're just checking at x = 0, nowhere else.
Continuous.
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, at x = -1
, at x = 0