Question

which step comes first in a standard algorithm for graphing a polynomial?
plot points from a value table
sketch the graph using all features
determine end behavior of the graph
find the real zeros and y - intercept

Explanation:

To graph a polynomial, the first step in the standard algorithm is to determine the end - behavior of the graph. This is because understanding the end - behavior (how the graph behaves as \(x\to\pm\infty\)) gives us a general shape of the graph at the "ends" and provides a foundation for further steps like finding zeros, plotting points, etc. Plotting points from a value table, sketching the graph with all features, and finding real zeros and the y - intercept come after we have an idea of the end - behavior.

Answer:

Determine end behavior of the graph