Question

Which polynomial(s) could have the following end behavior: as x→∞, f(x)→∞, and as x→−∞, f(x)→∞?

There may be more than one correct answer. Select all correct answers.

ax
−ax^5+bx^2+cx
ax^6
ax^2−b
ax^4−bx^3−cx^2−dx+e
ax^3+bx^2+c

this was so briefly went over in my notes...just wondering if I can get input how to know which is related to the end behavior formula given

Answer 1

any polynomial of even degree, with positive leading coefficient, will exhibit the required behavior.

Think of x^2. It goes up on both ends. Higher even degree will too, possibly with some wiggles near where it crosses the x-axis.