Overview of asymptotes

The video tutorial explains the concept of asymptotes, focusing on horizontal and vertical asymptotes. It describes how graphs approach these lines without crossing them. The tutorial covers methods to find asymptotes in rational functions, using examples to illustrate the process. It also discusses the significance of leading coefficients in determining horizontal asymptotes.

What is the main characteristic of a horizontal asymptote in a graph?

• The graph intersects the line at multiple points.

• The graph approaches the line but never touches it.

• The graph crosses the line at infinity.

• The graph oscillates around the line.

When a graph approaches zero from both positive and negative directions, what type of asymptote is being described?

• Horizontal asymptote

• Curved asymptote

• Vertical asymptote

• Diagonal asymptote

How do you determine the vertical asymptotes of a rational function?

• By setting the numerator equal to zero

• By setting the denominator equal to zero

• By finding the derivative of the function

• By solving for the x-intercepts

What happens to the graph of a function at a vertical asymptote?

• It becomes undefined.

• It oscillates around the asymptote.

• It approaches the asymptote but never crosses it.

• It crosses the asymptote.

In the context of horizontal asymptotes, what does it mean if the degree of the numerator is less than the degree of the denominator?

• The horizontal asymptote is determined by the leading coefficients.

• The horizontal asymptote is y = 1.

• There is no horizontal asymptote.

• The horizontal asymptote is y = 0.

What is the horizontal asymptote when the degrees of the numerator and denominator are equal?

• There is no horizontal asymptote

• y = the ratio of leading coefficients

• y = 1

• y = 0

If the degree of the numerator is greater than the degree of the denominator, what can be said about the horizontal asymptote?

• The horizontal asymptote is y = 0.

• There is no horizontal asymptote.

• The horizontal asymptote is y = 1.

• The horizontal asymptote is determined by the leading coefficients.

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

• By dividing the leading coefficients

• By setting the numerator equal to zero

• By finding the x-intercepts

• By setting the denominator equal to zero

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

• y = 0

• y = 3/2

• y = 1

• There is no horizontal asymptote

In the function f(x) = x^3 / (x - 1), what is the horizontal asymptote?

• y = 0

• y = 1

• y = x

• There is no horizontal asymptote