SOLUTION: Please help me determine if this is true or false and why? A rational function must have at least one vertical asymptote. How come no vertical asymptote exists when an examin

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Question 1054729: Please help me determine if this is true or false and why?
A rational function must have at least one vertical asymptote.
How come no vertical asymptote exists when an examination might show that there is one?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Not always. A rational function may be either simplifyable or not, meaning specifically REDUCIBLE as a fraction, or not. If reducible, then this could lead to a missing point or hole in the graph.


Assuming system%28a%3C%3Eb%2Cb%3C%3Ec%29,
%28x-a%29%28x-b%29%2F%28x-c%29=%28x%5E2-ax-bx%2Bab%29%2F%28x-c%29
Vertical asymptote for x=c.

%28x-a%29%28x-b%29%28x-c%29%2F%28x-b%29
NO VERTICAL ASYMPTOTE.
Instead, there is no point in the graph at x=b.