The line is a horizontal asymptote of a function if the outputs of the function get closer and closer to as the inputs get larger and larger in either the positive or negative direction. This means the graph gets closer and closer to the line as you move to the right or left along the -axis.
A rational function is a function defined by a fraction with polynomials in the numerator and denominator. Rational functions include polynomials because a polynomial can be written as a fraction with denominator 1.
The line is a vertical asymptote for a function if is undefined at and its outputs get larger and larger in the negative or positive direction when gets closer and closer to on each side of the line. This means the graph goes off in the vertical direction on either side of the line.
