Question:
write a rational function with no vertical asymptotes and no holes. explain.
Solution:
Let the following rational function:
[tex]f(x)\text{ = }\frac{x^3+2x^2-8x}{x^2+1}[/tex]
notice that the denominator is never zero:
[tex]x^2+\text{ 1 > 0}[/tex]
so there are no vertical asymptotes and no holes. (You need zeros in the denominator for those). The graph is shown below.
