Addition of functions: the Polynomial Form
Extension: polynomials
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Linear and quadratic functions
are part of a wider family of functions called "polynomials." The
correspondence rules of these functions are different from those
of quadratic functions in that they contain powers of x
that are higher than 2. For example:
f(x) = 2x³ + x² - 3x + 5
This task examines the graphs
of various polynomials.
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Use the Polynomials tool
to display polynomials and examine their properties.
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What do graphs of polynomials look like?
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| Examine graphs of polynomials for different parameter
values and sketch a collection of different shapes these graphs
can assume for polynomials of degrees 3, 4, and 5.
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In what ways are graphs of different polynomials of the same degree
similar? In what ways are they different?
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In what ways are graphs of polynomials of different degrees
similar? In what ways are they different?
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Describe interesting phenomena you encountered.
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