Question

Describe the end behavior and graph of f(x)=3+x^6

Answer 1

hyperbole. it goes to infinity

Answer 2

And it opens upwards?

Answer 3

use this
http://graph.tk/

Answer 4

Think of letting \(x\to\infty\) -- clearly we know \(x^6\to\infty\) as well hence our function will go off to infinity to the right. For the left-end behavior, consider \(x\to-\infty\) but because \(x^6\) is an even power of \(x\), the sign is ignored and we get \(x^6\to\infty\) once again; our function goes off to infinity to the left as well: