91Ó°ÊÓ

Graph the function in the standard viewing window and explain why that graph cannot possibly be complete. $$f(x)=.001 x^{5}-.01 x^{4}-.2 x^{3}+x^{2}+x-5$$

In Exercises \(1-54,\) perform the indicated operation and write the result in the form \(a+b i\). $$\frac{2+3 i}{i}$$

Analyze the function algebraically. List its vertical asymptotes, holes, y-intercept, and horizontal asymptote, if any. Then sketch a complete graph of the function. $$f(x)=\frac{2 x-3}{2 x}$$

Find a polynomial f(x) with real coefficients that satisfies the given conditions. Some of these problems have many correct answers. Degree \(3 ;\) roots -3,0,\(4 ; f(5)=80\)

Solve the inequality. Find exact solutions when possible and approximate ones otherwise. $$x^{3}-x \geq 0$$

$$\text { In Exercises } 29-40, \text { find all real roots of the polynomial.}$$ $$2 x^{3}-x^{2}-13 x-6$$

Find the rule of the quadratic function whose graph satisfies the given conditions. Vertex at (0,0)\(;\) passes through (2,12)

Find the remainder when \(f(x)\) is divided by \(g(x),\) without using division. $$f(x)=x^{10}+x^{8} ; \quad g(x)=x-1$$

In Exercises \(1-54,\) perform the indicated operation and write the result in the form \(a+b i\). $$\frac{1}{i(4+5 i)}$$

Analyze the function algebraically. List its vertical asymptotes, holes, y-intercept, and horizontal asymptote, if any. Then sketch a complete graph of the function. $$f(x)=\frac{x}{x(x-2)(x-3)}$$