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.

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.

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}.

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.

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.

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.

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.

Front

Solve for x: 2x + 3 = 3.

Back

x = 0.

Front

Back

The asymptotes are x=2 and y=1.

Front

Back

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