Polynomials and Power Functions

Question

What is the end behavior of the function

f(x)=3x^2+4x^3+x+3 using limits?

Answer 1

The highest power term is 4x^3 which will determine the end behavior. As x becomes more and more positive the function increases in value and as x becomes more and more negative the function becomes more negative so

As x approaches + infinity y approaches + infinity and

as x approaches - infinity y approaches - infinity