Question

Molly is on a game show. To win $1,000,000, she must answer this question: What key features are necessary—and how are the features used—to create the sketch of a polynomial function? What is Molly's winning answer? Explain in complete sentences.

Answer 1

- Find the y-intercept
- Find the roots (i.e. x - intercepts)
- Determine where the function increases and where it increases, along with the maximum and minimum values.
- Determine where the function changes concavity along with the inflection points.
- Determine the special points, where the value of the function is not defined and try to find the limit when the value of x approachs to this values
- Determine the limits of the function when x approachs to positive infinity and negative infinity

- For some of those steps you need to know some concepts of calculus: limits and derivatives along with the rules that let you know if a point is a maximum, a minimum or an inflection point.

With that information you can sketch a polynomial function.