Question

Explain the difference between the graphs of polynomial functions with a degree of 3 that have a positive leading coefficient and the graphs of those

Complex numbers
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asked 2021-06-21
Explain the difference between the graphs of polynomial functions with a degree of 3 that have a positive leading coefficient and the graphs of those with a negative leading coefficient.

Answers (1)

2021-06-22
The difference is in end behavior of those graphs.
Consider the function y=f(x) with a positive leading coefficient. Its end behavior is: \(\displaystyle{x}\to-∞\to{y}\to-∞\)
\(\displaystyle{x}\to∞\to{y}\to∞\)
Consider the function y=f(x) with a negative leading coefficient. Its end behavior is: \(\displaystyle{x}\to-∞\to{y}\to∞\)
\(\displaystyle{x}\to∞\to{y}\to-∞\)
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