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© Dr. Laura J. Pyzdrowski
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In this laboratory, you will learn about polynomial functions. A polynomial function is a function that has an equation of the form
f(x) = an xn + an-1 xn-1 + ... + a1 x + a0.
In this equation, an, an-1, ... a1, a0
represent numerical coefficients that are real numbers. Also in this equation,
the exponents of x are positive integers. You may remember that a quadratic
function is a special type of polynomial function and is sometimes written in
the form y = ax2 + b x + c. Notice that a quadratic function may
also be written in the form f(x) = a2x2 + a1x +
a0.
In this laboratory, you will explore the complete graphs of polynomial functions.
A complete graph of a function is one that depicts intercepts, end behavior
and basic shape. Remember that in order to show end behavior of a function,
it is necessary to show what happens to the range or functional values as the
domain values approach plus or minus infinity. Sometimes to determine end behavior,
we simply ask, “What happens to the y values as the x values approach
either
infinity or negative infinity?” When you are finished with this laboratory
you should be able to make a complete graph of polynomial functions that are
written in factored form. You should be able to do this by using analytical
and numerical skills.
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