Today's soundtrack is Carcass: Heartwork, an album that surprised me the first time I heard it, because I only knew them as a grindcore band, and here they were with some awesome melodic death metal. It's a great album.
This afternoon, I'm learning how to graph rational (fraction) functions and their reciprocals. Asymptotes are seen often in this lesson.
To find the vertical asymptote, we just look at the restrictions on x in the domain of the function. To find the horizontal asymptote, we can substitute extremely large positive and negative values for x and see what value y trends toward. To find our horizontal asymptote, we must first look at the terms of the rational function. If the highest-degree variable is in the denominator, the horizontal asymptote will always be y = 0. If the numerator and denominator have the same highest term, then we can cancel those terms out; y will equal the ratio of the coefficients.
PS: I made this meme today:
