Power Functions and Polynomial Functions · Exercise 63

Use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is 1 or –1. There may be more than one correct answer.

The $y-$ intercept is $\left(0,0\right).$ The $x-$ intercepts are $\left(0,0\right),\left(2,0\right).$ Degree is 3.
End behavior: $\text{as}x\to -\infty$,$f\left(x\right)\to -\infty$,$\text{as}x\to \infty$,$f\left(x\right)\to \infty .$

OpenStax, Precalculus 2e · §3.3 Power Functions and Polynomial Functions · Exercise 63