Question

Identify the asymptotes, removable discontinuities, and intercepts for the graph of each function.

1. z(x)= x^2-7x-8 / x^3+64

2. f(x)= 2x^3-3x+1 / x^3 -5x +7

Answer 1

How far did you get with these?

Answer 2

\[z(x)= \frac{x^2-7x-8}{x^3+64}\\
f(x)= \frac{2x^3-3x+1}{x^3 -5x +7}\]

Answer 3

I dont know how to even start

Answer 4

Factor things. Any factor on the top can be a 0 so an intercept. Any 0 on the bottom can be invalid, so an asymptote. BUT: If a factor is on both the top and bottom it is removable.