Problem
Show Intro/Instructions Suppose that $f(x)=-x^{3}+9 x^{2}-20 x$ a. What is the function's leading term? Preview b. What is the function's degree? Preview 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 $x \rightarrow \infty, f(x) \rightarrow$ Preview ○ As $x \rightarrow-\infty, f(x) \rightarrow$ Preview d. What is the vertical intercept for $f$ ? $y=$ Preview
Solution
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 \(\boxed{-x^{3}}\).
