The function will behave like $3x^4$.
Work Step by Step
Consider the graph: $f(x)=3x^4−x^3+5x^2−2x−7$ When considering behavior at infinity, we look at the highest degree of $x$ in the function. At infinity, the lower degrees of $x$ will be negligible comp,ared to the larger degrees of x. We see that the term with the highest degree is $3x^4$. This means that the function will behave like $3x^4$.