Question

Which best describes the graph of the cubic function f(x) = x^3 +x^2 +x +1?

A. x increases, y increases along the entire graph.

B. As x increases, y increases, decreases, and then increases again.

C. As x increases, y decreases, increases and then decreases again.

D. As x increases, y decrease along the entire graph. ​

Answer 1

A.

Explanation:

Now since the degree is odd (3 in this case) and the leading coefficient is positive (1), then the end behavior is going to be:

for left-end behavior, it is down

for right-end behavior, it is up

We are going to definitely have some increasing action going on because it goes from down to up reading from left to right.

Let's graph it in our ti-84's or whatever you have.

This is a very rough graph but you can see it is just increasing on the entire domain. This means reading the graph from left to right, there is only rise.

I can give you an answer with calculus in it if you prefer.