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Section 9.7 Summary of Polynomial Functions
Subsection 9.7.1 Summary of Graphing a Polynomial Function
End behavior . Find the end behavior of the polynomial, based on the degree and leading coefficient.
y-Intercept : Find the
\(y\) -intercept, by evaluating
\(f(0)\) (setting
\(x = 0\) and solving for
\(y\) ).
x-Intercept(s) : Find any
\(x\) -intercepts, by finding the zeros of the polynomial (setting
\(y = 0\) and solving for
\(x\) ). Use a scientific calculator, or the integral zero theorem / rational root theorem. See
Subsection 9.5.3 .
Multiplicity . Note the multiplicity of each zero. See
Table 9.4.4 .
Plot the
\(x\) -intercepts and
\(y\) -intercept.
Plot additional points between zeros (for more detail, if necessary).
Connect all of the points with a smooth curve, while respecting the end behavior and multiplicity at each zero.
