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How many vertical asymptotes does the equation \(y=\frac{x-1}{x^2+6x-7}\) have?

 Aug 28, 2018
 #1
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A vertical asymptote will  potentially  occur  where an x value makes the denominator of this rational function  = 0

 

To find these possibilities....set the denominator   =  0

 

x^2 + 6x  - 7   =  0

 

(x + 7) ( x - 1)    = 0

 

Setting both factors to 0 and solving for x produces   x  = -7  and  x  = 1

 

However.... since the  numerator  also  has the  factor (x -1), we will have a "hole"  at x  = 1

 

The only  true vertcal asymptote    will be at   x  =  -7

 

See the graph  here :  https://www.desmos.com/calculator/ohkiuoni6o

 

 

cool cool cool

 Aug 28, 2018

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