Describe the right­hand and left­hand behavior of the graph of the polynomial function. f(x)=x^5-x^2+2

Question

 Describe the right­hand and left­hand behavior of the graph of the polynomial function. f(x)=x^5-x^2+2

Answer 1

Since this polynomial is of degree 5 (odd), and since the sign of the leading term (degree 5) is positive, then this graph will RISE toward +infinity as x goes farther & farther to the right, and the graph will FALL toward -infinity as x goes farther & farther to the left.  This is a general fact that should be memorized.

 

For even degree polynomials, both end behaviors are in the same direction: upward if leading sign is positive, otherwise downward.