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Suppose that $f(x)=-x^{3}+9 x^{2}-20 x$
a. What is the function's leading term?
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b. What is the function's degree?
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c. What is the function's end behavior? (That is, does $f(x)$ increase or decrease without bound as $x$ increases or decreases without bound?)
ค As $x \rightarrow \infty, f(x) \rightarrow$
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○ As $x \rightarrow-\infty, f(x) \rightarrow$
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d. What is the vertical intercept for $f$ ?
$y=$
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Answer
So, the leading term of the function $f(x)=-x^{3}+9 x^{2}-20 x$ is \(\boxed{-x^{3}}\).
Step 1 ：The leading term of a polynomial function is the term with the highest degree.
Step 2 ：In this case, the function is $f(x)=-x^{3}+9 x^{2}-20 x$.
Step 3 ：The term with the highest degree in this function is $-x^{3}$.
Step 4 ：So, the leading term of the function $f(x)=-x^{3}+9 x^{2}-20 x$ is \(\boxed{-x^{3}}\).
