91Ó°ÊÓ

Find all real zeros of the polynomial function. $$g(x)=8 x^{4}+28 x^{3}+9 x^{2}-9 x$$

(a) use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero, and (b) use the zero or root feature of the graphing utility to approximate the real zeros of the function. Verify your answers in part (a) by using the table feature of the graphing utility. \(g(x)=3 x^{4}+4 x^{3}-3\)

Write a rational function that has the specificd characteristics. (There are many correct answers.) (a) Vertical asymptote: \(x=-2\) Slant asymptote: \(y=x+1\) Zero of the function: \(x=2\) (b) Vertical asymptote: \(x=-4\) Slant asymptote: \(y=x-2\) Zero of the function: \(x=3\)

Find all real zeros of the polynomial function. $$h(x)=x^{5}+5 x^{4}-5 x^{3}-15 x^{2}-6 x$$

(a) use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero, and (b) use the zero or root feature of the graphing utility to approximate the real zeros of the function. Verify your answers in part (a) by using the table feature of the graphing utility. \(h(x)=x^{4}-10 x^{2}+2\)

(a) use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero, and (b) use the zero or root feature of the graphing utility to approximate the real zeros of the function. Verify your answers in part (a) by using the table feature of the graphing utility. \(f(x)=x^{4}-3 x^{3}-4 x-3\)

Find all real zeros of the polynomial function. $$f(x)=8 x^{5}+6 x^{4}-37 x^{3}-36 x^{2}+29 x+30$$

Simplify the expression. $$\left(\frac{x}{8}\right)^{-3}$$

Find all real zeros of the polynomial function. $$g(x)=4 x^{5}+8 x^{4}-15 x^{3}-23 x^{2}+11 x+15$$

(a) use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero, and (b) use the zero or root feature of the graphing utility to approximate the real zeros of the function. Verify your answers in part (a) by using the table feature of the graphing utility. \(f(x)=x^{3}-4 x^{2}-2 x+10\)