Oblique Asymptotes (4.9.5)

Question 1

• An asymptote is a line that the graph of a function approaches but never touches.

Answer 1

• An asymptote is a line that the graph of a function approaches but never touches.

Question 2

• An oblique asymptote is an asymptote that is a slanted line (the line is neither vertical nor horizontal). The equation of this asymptote is the quotient (ignoring the remainder) when the numerator is divided by the denominator in a rational function where the numerator’s degree is equal to the denominator’s degree + 1.

Answer 2

• An oblique asymptote is an asymptote that is a slanted line (the line is neither vertical nor horizontal). The equation of this asymptote is the quotient (ignoring the remainder) when the numerator is divided by the denominator in a rational function where the numerator’s degree is equal to the denominator’s degree + 1.

Question 3

• If a rational function is equivalent to a linear function when this rational function is written in simplest form, the graph will be a line with at least one hole. The x-coordinate of a hole is found by setting each of the denominator’s removed factors equal to 0 and solving for x.

Answer 3

• If a rational function is equivalent to a linear function when this rational function is written in simplest form, the graph will be a line with at least one hole. The x-coordinate of a hole is found by setting each of the denominator’s removed factors equal to 0 and solving for x.