Question

Graph each of the following functions:

$$\begin{gathered} \frac{x^2}{x-1}, \\ \frac{x^4}{x-1}, \\ \frac{x^6}{x-1}, \\ \frac{x^8}{x-1} \end{gathered}$$

What similarities do you see? What differences?

Short answer

They all have same vertical asymptote, same intercepts and same minimum value at $x=0$.

They have different different oblique asymptotes and different maximum values.

Step-by-step solution

Step 1. The graph of x2x-1 is

Step 2. The graph of x4x-1 is

Step 3. The graph of x6x-1 is

Step 4. The graph of x8x-1 is

Step 5. The similarities and differences in their graphs.

They have same vertical asymptote, same intercepts and same minimum value at $x=0$.

They have different oblique asymptote and different maximum value.