Horizontal Asymptote:A horizontal asymptote is a horizontal line (y=b, wherebis a constant) that the graph of a function approaches, but does not touch. To find the horizontal asymptote of a function, we use the following rules: Rule 1: If the degree of the denominator i...
We can write these functions if we are given the vertical and horizontal asymptotes. For the vertical asymptotes, we follow the rule: if x = k is a vertical asymptote then the rational function will have the factor (x - k) in the denominator. For the horizontal asymptotes, if our ...
First, the function is undefined when x = –1. So the graph of x = –1 becomes a vertical asymptote. Second, find whether any horizontal asymptotes exist. To do this, solve the equation for x and see whether any values for y would make the new equation undefined. It may not always...
Thelinex=aisaverticalasymptoteofthegraphofafunctionfiff(x)increasesordecreaseswithoutboundasxapproachesa.f(x)asxa+ yffax=axaxx=a f(x)asxay Thus,f(x)orf(x)-asxapproachesafromeithertheleftortheright.Definitionofa VerticalAsymptote Thelinex=aisaverticalasymptote...
1 2 3 x a x x x Horizontal Asymptotes A Horizontal Asymptote to a function is like what the Pirate’s Code is in the “Pirates of the Caribbean”, its more of a guideline than a rigid rule, in the sense that the a horizontal asymptote is a line or a curve that the function ...
(I.1.16). The function crosses the y-axis at f (0) = 1. As the function cannot stay constant at 1, this suggests that there is a turning point for negative values of x. So, we need to take the derivative using the product rule (it is simpler to use that than blindly using the...
function behaves. These include, zeros (crosses the x axis) of the rational function point discontinuities (holes), vertical and horizontal asymptotes. Zeros (where the function crosses the x-axis) Zero’s occur when there are x (domain) values that cause the numerator to equal zero (as ...