What do you call an asymptote that is neither vertical nor horizontal?
slant; asymptote
We want to complete the sentence.
For the rational function f(x)=N(x)/D(x), if the degree of N(x) is exactly one more than the degree of D(x), then the graph of f has a (or oblique) .
Let's consider an example rational function that has the degree of N(x) that is exactly one more than the degree of D(x).
f(x) = x^2-x - 2/x^1-1
Let's take a look at the graph of this function.
The graph of the function has one vertical asymptote and one slant asymptote. The degrees of N(x) and D(x) do not matter when finding vertical asymptotes. Vertical asymptotes occur at the zeros of the denominator. However, the slant asymptote exists if and only if the degree of N(x) is exactly one more than the degree of D(x).
For the rational function f(x)=N(x)/D(x), if the degree of N(x) is exactly one more than the degree of D(x), then the graph of f has a slant (or oblique) asymptote.
