Answer
a. The polynomial function's graph falls to the left end and rises to the right end.
b. Graph $III$
Work Step by Step
End-Behaviour of a Polynomial
- Polynomial function of odd degree and positive leading coefficient falls to the left end and rises to the right end.
- Polynomial function of odd degree and negative leading coefficient rises to the left end and falls to the right end.
- Polynomial function of even degree and positive leading coefficient rises to the left end and right end.
- Polynomial function of even degree and negative leading coefficient falls to the left end and right end.
a.
In this case, $P(x)=x^3-4x$, the function is of odd degree and positive leading coefficient. therefore, the polynomial function's graph falls to the left end and rises to the right end.
b. The graph that matches the description is Graph $III$.
