Algebra 85 - Building Polynomial Functions

The video tutorial introduces polynomial functions, explaining their structure and how monomials form them. It discusses the impact of monomial coefficients on graph shapes, including vertical stretching, compressing, and reflecting. The tutorial explores how adding monomials affects polynomial graphs, focusing on end behavior and direction changes. By adding terms with different exponents, the video demonstrates how complex graphs with multiple direction changes are created. The tutorial concludes with a discussion on sketching polynomial graphs without digital tools.

Explain the concept of 'in behavior' of a polynomial graph.

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What is the effect of changing the coefficients of the terms in a polynomial function?

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How can the individual monomial functions affect the overall shape of a polynomial graph?

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What challenges might arise when sketching the graph of a polynomial function without technology?

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