To find a rational function's vertical asymyptotes, you need to find when the denominator is zero. So when is the denominator x² + 3x - 4 zero? We set that denominator equal to zero.
x² + 3x - 4 = 0
This second degree equation factors. We want a pair of numbers that multiply to 4, and there are only two pairs: 2 and 2, 1 and 4. We want the sum to 3, and one must be negative. -2 and 2 add to zero, -4 and 1 add to -3, -1 and 4 add to 3. The last one is the pair.
x² + 3x - 4 = 0
(x + 4) (x - 1) = 0
x = -4 or x = 1
So the function's vertical asymptotes are at x = 1 and x = -4.
The hundreds digit is twice as large as the ones digit. 3 doubled is 6, 6 doubled is 12, and 9 doubled is 18. Since 6 is the only option that is one digit, the hundreds digit must be 6 and the ones digit must be 3. The tens digit is five less than the hundreds digit.
