91Ó°ÊÓ

Solve the polynomial inequality. $$ 2 x^{4}+2 x^{3} \leq 12 x^{2} $$

Transformations Use transformations of the graph of either \(f(x)=\frac{1}{x}\) or \(h(x)=\frac{1}{x^{2}}\) to sketch a graph of \(y=g(x)\) by hand. Show all asymptotes. Write \(g(x)\) in terms of either \(f(x)\) or \(h(x)\) $$ g(x)=-\frac{2}{(x-1)^{2}} $$

Evaluate \(f(x)\) at the given \(x\) Approximate each result to the nearest hundredth. $$ f(x)=x^{3 / 2}-x^{1 / 2}, \quad x=50 $$

Transformations Use transformations of the graph of either \(f(x)=\frac{1}{x}\) or \(h(x)=\frac{1}{x^{2}}\) to sketch a graph of \(y=g(x)\) by hand. Show all asymptotes. Write \(g(x)\) in terms of either \(f(x)\) or \(h(x)\) $$ g(x)=\frac{1}{x^{2}}-1 $$

Evaluate \(f(x)\) at the given \(x\) Approximate each result to the nearest hundredth. $$ f(x)=x^{5 / 4}-x^{-3 / 4}, \quad x=7 $$

Solve the polynomial inequality. $$ x^{3}+6 x^{2}+9 x>0 $$

Transformations Use transformations of the graph of either \(f(x)=\frac{1}{x}\) or \(h(x)=\frac{1}{x^{2}}\) to sketch a graph of \(y=g(x)\) by hand. Show all asymptotes. Write \(g(x)\) in terms of either \(f(x)\) or \(h(x)\) $$ g(x)=\frac{1}{(x+1)^{2}}-2 $$

Solve the polynomial inequality graphically. $$ x^{3}-7 x^{2}+14 x \leq 8 $$

Solve the polynomial inequality graphically. $$ 2 x^{3}+3 x^{2}-3 x<2 $$

Transformations Use transformations of the graph of either \(f(x)=\frac{1}{x}\) or \(h(x)=\frac{1}{x^{2}}\) to sketch a graph of \(y=g(x)\) by hand. Show all asymptotes. Write \(g(x)\) in terms of either \(f(x)\) or \(h(x)\) $$ g(x)=1-\frac{1}{(x-2)^{2}} $$