DLD 10-4

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It is determined by the values that make the denominator of a rational function equal to zero.

Front

How do you find vertical asymptotes in a rational function?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the end behavior of the function.

Front

How do you determine horizontal asymptotes for rational functions?

Back

For rational functions, compare the degrees of the numerator and denominator: If the degree of the numerator is less than the denominator, y = 0 is the horizontal asymptote. If they are equal, divide the leading coefficients.

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator. It can be found using polynomial long division.

Front

Back

Front

What is the definition of a rational function?

Back

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator is zero, as division by zero is not possible.

Front

Back

Front

What is the significance of finding the vertical asymptote?

Back

Finding the vertical asymptote helps identify the values of x where the function is undefined and indicates where the function may approach infinity.