Limits at Infinity and Asymptotes

Horizontal asymptotes from limits at infinity

Vertical asymptotes

Oblique asymptotes

Transcendental end behavior

The rational function (3x^2 + x)/(2x^2 - 5) has what horizontal asymptote?

The function (x^2 - 1)/(x^2 - 1) would reduce to 1 everywhere except at x = plus or minus 1. What does the graph have at those points?

Near x = 1, the function 1/(x - 1) has what one-sided limit behavior?

Polynomial division of (x^2 + 2x)/(x - 1) gives x + 3 plus a remainder term. What line is the oblique asymptote?

Which pair correctly states the two end behaviors of f(x) = e^x?

The function sin(x)/x approaches 0 as x approaches infinity, so y = 0 is a horizontal asymptote. What else is true of this function?

What is lim x to infinity of 1/x? Answer with a number.

The function 1/(x - 2)^2 has an unbounded blow-up at one point. At what x does the vertical asymptote occur? Answer with a number.

An oblique asymptote occurs when the numerator's degree exceeds the denominator's by exactly one. If the denominator has degree 2, what numerator degree gives an oblique asymptote? Answer with a number.

As x approaches infinity, arctan x approaches pi/2. What horizontal asymptote does the graph have on the right? Answer like y = pi/2.