Identify the holes, vertical asymptotes and horizontal asymptotes of f(x)=x²+7x+12/-x²-3x+4
1 answer:
<h3>Answer:</h3>
- hole: x = -4
- vertical asymptote: x = 1
- horizontal asymptote: y = -1
The function factors as ...
... f(x) = -(x+3)(x+4)/((x-1)(x+4)) = -(x+3)/(x-1) . . . . x ≠ -4
and the quotient is ...
... f(x) = -(1 +4/(x-1))
... f(x) = -1 -4/(x-1) . . . . . x ≠ -4
This has a hole at x = -4 (where the denominator factor cancels the numerator factor), a vertical asymptote at x=1 (where the denominator is zero), and a horizontal asymptote at y = -1 (the value of the function for large values of x).
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We can rewrite that without the primes and combine the powers of 2.
Let's graph these and see if we're close,
Plot y= (1/4)^x, y= - (1/4)^{x}, y = - 2^{1-x}
