Answer
See the explanation
Work Step by Step
a. If $r(x)=\frac{P(x)}{Q(x)}$ is a rational function in which the degree of the numerator is one more than the degree of the denominator, we can use division algorithm to express the function in the form $r(x)=ax+b + \frac{S(x)}{Q(x)}$, where the degree of $S$ is less than the degree of $Q$ and $a\ne 0$. This means that as $x \rightarrow \pm \infty$, $\frac{S(x)}{Q(x)} \rightarrow 0$. Therefore, for large values of $|x|$ the graph of $y=r(x)$ approaches the line $y=ax+b$. In this situation, we say that $y=ax+b$ is a slant asymptote or an oblique asymptote.
b. The end behavior of a graph of a function is the way the graph behaves as $x$ approaches $\infty$ or $-\infty$. The end behavior of a function is equal to its horizontal, slant/oblique asymptotes or the quotient found using long division of the polynomials.
