Horizontal Asymptotes (4.9.2)

Question 1

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

Answer 1

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

Question 2

• To find the horizontal asymptotes of a rational function, consider the largest powers of x in the numerator and denominator:
1. If the largest power of x is in the denominator, the function has a horizontal asymptote at y = 0 (the x -axis).
2. If the largest power of x is in the numerator, the function has no horizontal asymptote.
3. If the powers of x are equal in the numerator and denominator, the function has a horizontal asymptote. Divide the
coefficients of the largest powers of x to find out where the asymptote is located.

Answer 2

• To find the horizontal asymptotes of a rational function, consider the largest powers of x in the numerator and denominator:
1. If the largest power of x is in the denominator, the function has a horizontal asymptote at y = 0 (the x -axis).
2. If the largest power of x is in the numerator, the function has no horizontal asymptote.
3. If the powers of x are equal in the numerator and denominator, the function has a horizontal asymptote. Divide the
coefficients of the largest powers of x to find out where the asymptote is located.