Question

If mc009-1.jpg and mc009-2.jpg, what is the degree of mc009-3.jpg?
2
3
5
6

Answer 1

I can’t see the three image files you named. Could you either upload them here or describe what each graph shows (number of turning points, x-intercepts, and the end-behavior left/right up or down)?

If you want to work it out yourself, here are the approaches depending on what each image represents:

- If mc009-3.jpg is the graph of a polynomial f(x):
- The number of turning points (local maxima/minima) ≤ degree − 1. So degree ≥ (turning points + 1).
- The end behavior (both ends up → even degree with positive leading coefficient; both ends down → even degree with negative leading coefficient; one end up and one end down → odd degree) tells you parity (even/odd).
- Combine parity and minimum degree to pick the smallest degree consistent with the graph (and choose among the options 2, 3, 5, 6).

- If mc009-1.jpg and mc009-2.jpg are graphs of f′ and f″ and mc009-3.jpg is f:
- deg(f) = deg(f′) + 1 = deg(f″) + 2. So determine the degree of f′ or f″ from their graphs (count zeros and end-behavior or turning points) and add as above.

Send the images or a description and I’ll pick the correct option and show the reasoning.