Do not omit parentheses in the numerator and denominator:
f(x)= (2x^2 + 7x + 12)/(2x^2 + 5x - 12)
The function is different without them.
All polynomials are continuous over ℝ.
For a rational function, where a polynomial is divided by another, vertical asymptotes occur at the zeroes of the denominator, or 2x²+5x-12 in the present case.
Factorize 2x²+5x-12 to get
(x+4)(2x-3)
Solve for
(x+4)=0 and (2x-3)=0 for the locations of vertical asymptotes.
Horizontal asymptotes are the limites of the function when x->-∞ or x->∞.
For the case of rational functions where the degree of the numerator equals that of the denominator, the limit reduces to the quotient of the leading terms, namely:
2x²/2x²=1
So the horizontal asymptote is at y=1.
Find all horizontal and vertical asymptotes of f(x)= 2x^2 + 7x + 12/
2x^2 + 5x - 12
1 answer