For the polynomials in the following exercise, state the degree and the number of terms, and describe the long-run behavior.

$$y=1-2 x^4+x^3$$

Use limits involving $\pm \infty$ to describe the asymptotic behavior of the function $f(x)=\frac{1}{3-x}$ from its graph.

Ultimately why does Chamberlain "believe in a British Empire"? How does he appear to view the rest of the world?

For the following question,

Graph the polynomial functions. Note $x$ - and $y$-intercepts, multiplicity, and end behavior.

$$k(x)=(x-3)^3(x-2)^2$$

For the following question,

Graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior.

$$f(x)=x^3-0.01 x$$

For the following key term or person, write a sentence explaining its connection to World War I: Zimmermann npte

In this exercise, find the transition points, intervals of increase/decrease, concavity, and asymptotic behavior. Then sketch the graph, with this information indicated.

$$y=x-x^{-1}$$

For the given polynomial function 'f' :

$f(x)=(x+1)^3(x-3)$

End behavior: Find the power function that the graph of f resembles for large values of |x|.

For the given polynomial function 'f' :

$$f(x)=(x-1)(x+4)(x-3)$$

End behavior: Find the power function that the graph of f resembles for large values of |x|.

Use limits involving $\pm \infty$ to describe the asymptotic behavior of the function $f(x)=\frac{3 x}{x-2}$ from its graph.

(a) Explain the options for resolving a bitter territorial dispute among nations in today's world. (b) Why are such problems so complicated?

For the following key term or person, write a sentence explaining its connection to World War I: trench warfare

For the following question,

Make tables to show the behavior of the function near the vertical asymptote and reflect the horizontal asymptote.

$$f(x)=\frac{x}{x-3}$$

Describe the end behavior of the function $f(x)=-\frac{1}{2} x^5$ using the leading coefficient and degree, and state the domain and range.