+884 How many vertical asymptotes does the equation \(y=\frac{x-1}{x^2+6x-7}\) have?
+128406 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
