+4622 How many vertical asymptotes does the graph of \(y=\frac{x-3}{x^2+7x-30}\) have?
+9481 Vertical asymptotes occur when y is undefined.
Y is undefined when the denominator is = 0.
So set the denominator = 0 to find which x values make y undefined.
x2 + 7x - 30 = 0
x2 + 7x + 49/4 = 169/4
x + 7/2 = ±13/2 - 7/2
x = 3 and x = -10
SO there are 2 values that make y undefined.
But from looking at a graph (or by taking the limit as x approaches 3) you can see that at x = 3 there is only a point discontinuity, not an asymptote.
So there is only 1 veertical asymptote at x = -10.
+37153 (x-3) (x-3)/[(x-3)(x+10)] = 1 /(x+10)
_____ =
x^2 +7x-30
So as x approaches -10 you will have an asymtope there at -10 One asymtope at x = -10
