91Ó°ÊÓ

Suppose that a polynomial function of degree 5 with rational coefficients has the given numbers as zeros. Find the other \(z e r o(s)\) $$-\frac{1}{2}, \sqrt{5},-4 i$$

Use synthetic division to find the function values. Then check your work using a graphing calculator. \(f(x)=2 x^{5}-3 x^{4}+2 x^{3}-x+8 ;\) find \(f(20)\) and \(f(-3)\)

Find the zeros of the polynomial function and state the multiplicity of each. $$f(x)=(x+5)^{3}(x-4)(x+1)^{2}$$

Find the zeros of the polynomial function and state the multiplicity of each. $$f(x)=-2(x-4)(x-4)(x-4)(x+6)$$

Find the zeros of the polynomial function and state the multiplicity of each. $$f(x)=x^{3}(x-1)^{2}(x+4)$$

Solve. $$11-x^{2} \geq 0$$

Graph the piecewise function. \(h(x)=\left\\{\begin{array}{ll}-x^{2}, & \text { for } x<-2 \\ x+1, & \text { for }-2 \leq x<0 \\ x^{3}-1, & \text { for } x \geq 0\end{array}\right.\)

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. $$-\sqrt{2}, 4 i$$

Make a hand-drawn graph. Be sure to label all the asymptotes. List the domain and the \(x\) -intercepts and the \(y\) -intercepts. Check your work using \(a\) graphing calculator. $$f(x)=\frac{x+3}{x^{2}-9}$$

Using the intermediate value theorem, determine, if possible, whether the function \(f\) has a real zero between a and \(b\). $$f(x)=x^{4}-2 x^{2}-6 ; a=2, b=3$$