91Ó°ÊÓ

Find a polynomial function \(f\) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of leading coefficient. Degree \(5 ;\) zeros: \(2 ;-i ; 1+i\)

In Problems \(25-32,\) use the given zero to find the remaining zeros of each polynomial function. $$ f(x)=x^{3}-5 x^{2}+9 x-45 ; \text { zero: } 3 i $$

Find the domain of each rational function. $$ F(x)=\frac{-2\left(x^{2}-4\right)}{3\left(x^{2}+4 x+4\right)} $$

Determine the maximum number of real zeros that each polynomial function may have. Then use Descartes' Rule of Signs to determine how many positive and how many negative real zeros each polynomial function may have. Do not attempt to find the zeros. $$ f(x)=x^{4}+5 x^{3}-2 $$

Determine the maximum number of real zeros that each polynomial function may have. Then use Descartes' Rule of Signs to determine how many positive and how many negative real zeros each polynomial function may have. Do not attempt to find the zeros. $$ f(x)=x^{5}+x^{4}+x^{2}+x+1 $$

Use the given zero to find the remaining zeros of each polynomial function. $$ f(x)=x^{4}-7 x^{3}+14 x^{2}-38 x-60 ; \text { zero: } 1+3 i $$

(a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. $$ Q(x)=3+\frac{1}{x^{2}} $$

List the potential rational zeros of each polynomial function. Do not attempt to find the zeros. $$ f(x)=x^{5}-2 x^{2}+8 x-5 $$

(a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. $$ R(x)=\frac{3}{x} $$

(a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. $$ H(x)=\frac{-2}{x+1} $$