Why do Pre-Calculus students need to learn graphing polynomial functions? They cannot find the local max/min yet. Should we postpone this topic in Calculus?
Thank you for your feedback!
It is true that a complete graph of polynomials (third degree and higher) cannot be drawn analytically at this point, but there is still a lot of valuable learning in creating a sketch with what we can find. My methodology for graphing polynomial functions allows them to connect the concepts of intercepts, multiplicities (of zeros), and end behavior into a coherent procedure that leads to a stronger overall understanding of this important class of function. I take the same stance with Rational Function as their graphs are not going to be 100% accurate but a great way to unify the various concepts.
Perhaps we should ponder the whole concept of teaching a separate precalculus course.
It's possible that students would benefit more from the introduction of precalculus topics as the concepts of limits, derivatives and integrals are being taught.
However, my personal opinion is that trigonometry should remain a separate course as a prerequisite for calculus.
I agree with Matthew. Pre-calculus students learn graphing polynomial functions to lay a foundation for understanding more complex concepts later on. While they may not yet be ready to find local maxima and minima, postponing this topic until calculus could hinder their mathematical development. By introducing graphing early, students become familiar with important features, terminology, and ideas, setting the stage for deeper understanding and success in higher-level math. Math is cumulative, and each concept builds upon the last, so it's essential to start laying the groundwork early on.
Thank you so much for your answer!
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