Question 255545: CAN YOU PLEASE HELP ME?!?!?
Describe the vertical asymptote(s) and hole(s) for the graph of
y= ((x-5)(x-2))/((x-2)(x+4))
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! division by zero is "Verbotten!", so when a term in the denominator (bottom) of the fraction is zero -- things happen
when x=-4, the x+4 term is zero ___ this results in a vertical asymptote at x=-4
___ since the sign of the denominator changes as x passes through -4, the direction of the asymptote also changes
___ it is upward (positive) below -4 and downward (negative) above -4
when x=2, the x-2 terms are zero ___ since there are terms in both the numerator AND denominator
___ this results in a "hole" in the graph at x=2
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