Flashcard 2.5

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is a slant asymptote?

Back

A slant (or oblique) asymptote is a diagonal line that the graph of a function approaches as x approaches positive or negative infinity, occurring when the degree of the numerator is one more than the degree of the denominator.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, the asymptote is y=\frac{leading coefficient of numerator}{leading coefficient of denominator}.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x=a where the function approaches infinity or negative infinity as x approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided that these values do not also make the numerator zero.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean if a function has no vertical asymptotes?

Back

If a function has no vertical asymptotes, it means that the denominator does not have any real roots that would cause the function to be undefined.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the degree of a polynomial in determining asymptotes?

Back

The degree of a polynomial helps determine the behavior of the function at infinity and the presence of horizontal or slant asymptotes.

Tags

CCSS.HSF-IF.C.7D

Front

Solve for x: 2x + 3 = 3.

Back

x = 0.

Tags

CCSS.7.EE.B.4A

Front

Back

The asymptotes are x=2 and y=1.

Tags

CCSS.HSF-IF.C.7D

Front

Back

The function has 2 vertical asymptotes at x=2 and x=-2.

Tags

CCSS.HSF-IF.C.7D