Question

If the rational function y=r(x) has the vertical asymptote x=2, then as x→2, either y→ (smaller value) or y→ (larger value).

a) True
b) False

Answer 1

The statement is true; as x approaches the vertical asymptote, the value of y in a rational function will tend to either a very large positive value or a very large negative value.

Step-by-step explanation:

If the rational function y=r(x) has the vertical asymptote x=2, then this statement is True: as x approaches 2, the function y will either approach a very large positive value or a very large negative value, which can be described as 'either y→ (smaller value) or y→ (larger value)'.

Vertical asymptotes occur in rational functions where the denominator equals zero and the function is undefined. In such a case, as the value of x approaches the asymptote, the value of y will increase towards positive infinity or decrease towards negative infinity. The direction in which y travels as x approaches the vertical asymptote depends on the behavior of the function on either side of the asymptote.