Finding the asymptotes

Finding the asymptotes

Assessment

Interactive Video

Mathematics

11th Grade - University

Hard

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The video tutorial explains how to find vertical and horizontal asymptotes of a function. It begins with an introduction to asymptotes, followed by detailed steps to determine vertical asymptotes by setting the denominator of a rational function to zero. The tutorial then covers horizontal asymptotes, focusing on comparing the degrees and leading coefficients of polynomials. The video concludes with a brief mention of slant asymptotes, which will be covered in another video.

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7 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary method to find vertical asymptotes of a rational function?

Find the derivative of the function

Solve for x-intercepts

Set the denominator equal to zero

Set the numerator equal to zero

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the example provided, what are the vertical asymptotes for the equation X^2 = 3?

X = 0

X = ±sqrt(3)

X = ±3

X = ±1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When comparing polynomials to find horizontal asymptotes, what should you compare?

The coefficients of the constant terms

The degrees and leading coefficients

The x-intercepts

The y-intercepts

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

No horizontal asymptote

y = 1

y = x

y = 0

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you find the horizontal asymptote when the degrees of the numerator and denominator are equal?

Subtract the coefficients

Multiply the coefficients

Divide the coefficients

Add the coefficients

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

y = x

No horizontal asymptote

y = 1

y = 0

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If the leading coefficients of the numerator and denominator are 3 and 4 respectively, what is the horizontal asymptote?

y = 4/3

y = 3/4

y = 1

y = 0