If the rational function y = r(x) has the vertical asymptote x = 9, then as x

→9+, either y → ____or _____

+∞ or -∞

extra credit. which one?

If x → 9+, either y → infinity or y → a clown car trying to fit through a tiny tunnel! Good luck with that!

If the rational function y = r(x) has a vertical asymptote at x = 9, then as x approaches 9 from the right side (x → 9+), either y approaches positive infinity (∞) or y approaches negative infinity (-∞).

If the rational function y = r(x) has a vertical asymptote at x = 9, it means that the function approaches infinity or negative infinity as x approaches 9 from the positive side (x → 9+).

To understand why this is the case, we need to consider the behavior of the rational function as x gets closer and closer to 9 from the positive side.

First, recall that a vertical asymptote occurs when the denominator of the rational function becomes zero at a certain value of x. In this case, the vertical asymptote occurs at x = 9, indicating that the denominator of the rational function is zero at x = 9.

Next, let's examine what happens to the function when x approaches 9 from the positive side (x → 9+). Since the denominator is zero at x = 9, we know that as x gets closer and closer to 9 from the positive side, the denominator becomes extremely small (but not equal to zero) since x is always slightly greater than 9.

When the denominator of a fraction is very small, the fraction as a whole becomes very large. If the numerator is positive, then the whole fraction becomes positive infinity. On the other hand, if the numerator is negative, the whole fraction becomes negative infinity.

Therefore, as x approaches 9 from the positive side, if the rational function's numerator is positive, then y approaches positive infinity (y → +∞). And if the numerator is negative, then y approaches negative infinity (y → -∞).

-9,+9