3.6 (1) --- Rational Functions

Question

If the rational function y = r(x)  has the vertical asymptote x = 1,

 then as x → 1⁺,  either

Y-->________ (smaller value)

Y-->________ (larger value)

Answer 1

For a rational function y = r(x) with a vertical asymptote at x = 1, as x approaches 1 from the right (x → 1⁺):

1. y → −∞ (the smaller value) if the function approaches negative infinity.
2. y → ∞ (the larger value) if the function approaches positive infinity.

This means the function y = r(x) can either decrease without bound (approaching −∞) or increase without bound (approaching ∞) as x gets closer to 1 from the right.

Hope this was helpful.