Asked by kelly
Find all horizontal and vertical asymptotes of f(x)= 2x^2 + 7x + 12/
2x^2 + 5x - 12
2x^2 + 5x - 12
Answers
Answered by
MathMate
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.
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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.