Question

Which of the graphs below represent the function f(x) = − x3 + 4x2 − x + 3? You may sketch the graph to compare.

Answer 1

the easy/cheat method would be to graph it and pick the one that matches, but to approach this problem more intelligently, we can look at two aspects of the graph

- if we plug in x = 0, we get f(x) = 3, which means the y-intercept is 3
- the sign of the leading coefficient is negative, and the degree (highest exponent) is odd, so the graph should go to negative infinity as x goes to negative infinity, and to positive infinity as x goes to positive infinity.

with that in mind, which graph do you think has these characteristics?