For this blog im going to review how to find the continuity of different functions like fractions and piecewise.
When you have a fraction you first have to factor the top and the bottom of the factor. If it is possible then you must cancel with what you got from factoring. After this you set what you have cancelled to zero and then you solve for x. in this case you would have a removable in the problem.
if you are unable to factor and cancel anything from the fraction you have you then set the denominator of the fraction equal to zero and from there you solve for x. you will get a number and whatever number you get with be the answer. In this case you will have a vertical asymptote or an infinite in the problem.
Another one is piecewise with a piecewise you have to plug in the x values to see if they are equal. If they are not equal it is a jump. If the two are equal but there is no equal under the less or greater sign it is a removable. A piecewise is a little more difficult to deal with but it can be solved easily. When solving for vertical asymptotes, there are 3 possible limits which can be found: infinity, negative infinity, or does not exist (DNE).
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