Algebra 2 Asymptotes Flashcards

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Questions and Answers

When do vertical asymptotes occur?

When the denominator equals zero

Will the vertical asymptotes ever cross? Why or why not?

False

How do you find the vertical asymptotes?

You set the denominator equal to zero

How are horizontal asymptotes found?

Evaluating the degree of the numerator and the degree of the denominator Signup and view all the answers

What are the three types of horizontal asymptotes?

Degree of the Denominator > Degree of the Numerator Signup and view all the answers

Describe the case when the Degree of the Denominator > Degree of the Numerator.

The horizontal asymptote is at y=0 Signup and view all the answers

Describe the case when the Degree of the Denominator = Degree of the Numerator.

The horizontal asymptote is found by dividing by the leading coefficient Signup and view all the answers

Describe the case when the Degree of the Denominator < Degree of the Numerator.

There is no horizontal asymptote Signup and view all the answers

When do holes occur?

When factors cancel Signup and view all the answers

When should you find the holes?

Before you name the asymptotes Signup and view all the answers

What is the first step in finding the coordinates of a hole?

Factor the numerator and denominator to see if any factors cancel Signup and view all the answers

What is the second step in finding the coordinates of a hole?

If two factors cancel, set one of the factors equal to zero to find the x-coordinate of the hole Signup and view all the answers

What is the third step in finding the coordinates of a hole?

Plug the x-value into the simplified equation to find the y-value Signup and view all the answers

When do x-intercepts occur?

Where the graph crosses the axis Signup and view all the answers

How do you find the x-intercepts?

Set the top equal to zero Signup and view all the answers

When do y-intercepts occur?

Where the function crosses the y-axis Signup and view all the answers

How do you find the y-intercepts?

Plug zero in for x Signup and view all the answers

What is end behavior?

What happens at the left and right ends of the graph Signup and view all the answers

What do you need to look for to determine the end behavior?

The horizontal asymptote Signup and view all the answers

What happens if there isn't a horizontal asymptote?

The end behavior will be... (L) X -> -infinity, F(X) -> -infinity; (R) X -> +infinity, F(X) -> +infinity Signup and view all the answers

Study Notes

Vertical Asymptotes

Occur when the denominator of a function equals zero.
Vertical asymptotes do not intersect the graph because the function is undefined at these points.
To find vertical asymptotes, set the denominator equal to zero.

Horizontal Asymptotes

Determined by comparing the degree of the numerator and denominator.
There are three scenarios for horizontal asymptotes based on the degree comparison:
- Degree of the denominator (bottom) > degree of the numerator (top): Asymptote at y=0.
- Degree of the denominator = degree of the numerator: Asymptote found by dividing the leading coefficients.
- Degree of the denominator < degree of the numerator: No horizontal asymptote exists.

Holes in the Graph

Occur when factors in the numerator and denominator cancel.
Holes should be identified before determining asymptotes.
Steps to find hole coordinates:
- Factor both the numerator and denominator to identify canceling factors.
- Set one of the canceled factors equal to zero to find the x-coordinate.
- Substitute the x-coordinate into the simplified equation to find the corresponding y-coordinate.

Intercepts

X-intercepts happen where the graph crosses the x-axis, found by setting the numerator equal to zero.
Y-intercepts occur where the function crosses the y-axis, determined by plugging zero into x.

End Behavior

Refers to the behavior of the graph as x approaches positive or negative infinity.
The presence of a horizontal asymptote is crucial for determining end behavior.
If there is no horizontal asymptote, the graph will approach infinity or negative infinity on either end:
- Left (L): As x approaches -infinity, f(x) approaches -infinity.
- Right (R): As x approaches +infinity, f(x) approaches +infinity.

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Description

Test your understanding of asymptotes in Algebra 2 with these flashcards. Learn about vertical and horizontal asymptotes, when they occur, and how to find them. This quiz will help reinforce key concepts critical for mastering functions in algebra.