91Ó°ÊÓ

(a) use a graphing utility to graph the function, (b) use the graph to approximate any \(x\)-intercepts of the graph, (c) set \(y=0\) and solve the resulting equation, and (d) compare the results of part (c) with any \(x\)-intercepts of the graph. $$y=4 x^{3}+4 x^{2}-8 x-8$$

Fill in the blanks. The ______ _______ _______ states that if \(f(x)\) is a polynomial of degree \(n(n>0),\) then \(f(x)\) has precisely \(n\) linear factors, \(f(x)=a_{n}\left(x-c_{1}\right)\left(x-c_{2}\right) \cdots\left(x-c_{n}\right),\) where \(c_{1}, c_{2}, \ldots, c_{n}\) are complex numbers.

When \(f(x) \rightarrow \pm \infty\) as \(x \rightarrow a\) from the left or the right, \(x=a\) is a _________ __________ of the graph of \(f\).

A ___ function is a second-degree polynomial function, and its graph is called a ___.

Fill in the blanks. A polynomial function of degree \(n\) has at most _________ real zeros and at most _________ turning points.

Fill in the blanks. In the Division Algorithm, the rational expression \(f(x) / d(x)\) is __________ because the degree of \(f(x)\) is greater than or equal to the degree of \(d(x)\)

Fill in the blanks. The test that gives a list of the possible rational zeros of a polynomial function is the ______ ______ test.

Fill in the blanks. A __________ _________ number has the form \(a+b i\), where \(a=0, b \neq 0\).

Fill in the blanks. The key numbers of a rational expression are its ____________ and its _____________ ______________.

When \(f(x) \rightarrow b\) as \(x \rightarrow \pm \infty, y=b\) is a ______ ______ of the graph of \(f\).