Question

What key features are necessary—and how are the features used—to create the sketch of a polynomial function?

Answer 1

Randy is taking his math SAT. To receive full credit, he 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 Randy's correct answer, so he receives full credit for the question? Explain in complete sentences.

Answer 2

Is there answers choices?

Answer 3

sadly, no

Answer 4

You need critical points and the nature of the curve between those points (increasing/decreasing). Maybe x and y components.

Answer 5

Okay so would the increasing/decreasing be slope?

Answer 6

Yes, a positive slope is increasing and negative is decreasing

Answer 7

okay do you know how to use them to make the function

Answer 8

or the sketch sorry

Answer 9

You would pretty much connect the dots (the dots being the critical points) with curves instead of lines, making sure the curve is oriented properly based on what you found for the derivative at those sections

Answer 10

A polynomial will always have a second derivative value as well that tells you the shape of the curve

Answer 11

But I'd use the first derivative critical points and work from there

Answer 12

Do you think that is all I need to add?

Answer 13

I can't think of anything else

Answer 14

But I think that would give you the whole graph