Question

Given the function f(x) = −3x3 + 9x2 − 2x + 3, what part of the function indicates that the left end starts at the top of the graph?

Answer 1

in general, end behavior of polynomials is determined by

1. the degree (highest exponent)
2. the sign of the leading coefficient (on the highest degree term, is the coefficient positive or negatve)

try and evaluate these for your polynomial and explain why this means that the left end starts at the top (a.k.a what kind of values the function takes when the x becomes increasingly negative)