What is the horizontal asymptote of R(x)=(3x^2-2x+4)/(x^2+1)?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $25.99Unlock all

Get ready for your Honors Mathematics 3 exam with our engaging quizzes. Use flashcards and multiple choice questions with explanations to enhance your study. Prepare effectively for the test!

Multiple Choice

What is the horizontal asymptote of R(x)=(3x^2-2x+4)/(x^2+1)?

Explanation:
When a rational function has the same degree in the numerator and denominator, its horizontal asymptote is the ratio of the leading coefficients. Here the leading terms are 3x^2 in the numerator and x^2 in the denominator, so as x grows large, R(x) behaves like 3x^2/x^2 = 3. This means the graph approaches the line y = 3 as x goes to ±∞. The other options don’t fit because y = 0 would come from a smaller degree in the numerator, and a negative value would require a negative leading ratio, which isn’t the case here.

When a rational function has the same degree in the numerator and denominator, its horizontal asymptote is the ratio of the leading coefficients. Here the leading terms are 3x^2 in the numerator and x^2 in the denominator, so as x grows large, R(x) behaves like 3x^2/x^2 = 3. This means the graph approaches the line y = 3 as x goes to ±∞. The other options don’t fit because y = 0 would come from a smaller degree in the numerator, and a negative value would require a negative leading ratio, which isn’t the case here.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy