91Ó°ÊÓ

If, as \(x \rightarrow-\infty\) or as \(x \rightarrow \infty,\) the values of \(R(x)\) approach some fixed number \(L,\) then the line \(y=L\) is a ________ ___________ of the graph of R.

Multiple Choice Given \(f(x)=3 x^{4}-2 x^{3}+7 x-2,\) how many sign changes are there in the coefficients of \(f(-x) ?\) (a) 0 (b) 1 (c) 2 (d) 3

If, as \(x\) approaches some number \(c,\) the values of \(|R(x)| \rightarrow \infty,\) then the line \(x=c\) is a _______ ___________ of the graph of R.

True or False A polynomial function of degree 4 with real coefficients could have \(-3,2+i, 2-i,\) and \(-3+5 i\) as its zeros.

In Problems 9-18, information is given about a polynomial function f whose coefficients are real numbers. Find the remaining zeros off. Degree \(3 ;\) zeros: \(3,4-i\)

If \(f\) is a polynomial function and \(x-4\) is a factor of \(f\) then \(f(4)=\) __________.

True or False If \(f\) is a polynomial function of degree 4 and if \(f(2)=5,\) then $$ \frac{f(x)}{x-2}=p(x)+\frac{5}{x-2} $$ where \(p(x)\) is a polynomial of degree 3 .

Information is given about a polynomial function f whose coefficients are real numbers. Find the remaining zeros off. Degree \(4 ;\) zeros: \(i, 3+i\)

Use the Remainder Theorem to find the remainder when \(f(x)\) is divided by \(x-c .\) Then use the Factor Theorem to determine whether \(x-c\) is a factor of \(f(x)\). $$ f(x)=4 x^{3}-3 x^{2}-8 x+4 ; x-2 $$

True or False If the degree of the numerator of a rational function equals the degree of the denominator, then the rational function has a horizontal asymptote.