Algebra 2 Asymptotes Flashcards

When do vertical asymptotes occur?

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

How do you find the vertical asymptotes?

How are horizontal asymptotes found?

What are the three types of horizontal asymptotes?

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

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

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

When do holes occur?

When should you find the holes?

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

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

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

When do x-intercepts occur?

How do you find the x-intercepts?

When do y-intercepts occur?

How do you find the y-intercepts?

What is end behavior?

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

What happens if there isn't a horizontal asymptote?

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.

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.