Question

for each function, determine whether it is a polynomial function.

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$$\begin{tabular}{|l|c|c|} \\hline \\multirow{2}{*}{function} & \\multicolumn{2}{c|}{is the function a polynomial?} \\\\ \\cline{2-3} & yes & no \\\\ \\hline (a) \\(v(x) = -9x\\) & & \\\\ \\hline (b) \\(f(x) = 7x^7 + 9x^4 + \\frac{x}{5}\\) & & \\\\ \\hline (c) \\(h(x) = 8x^9 + 0.9x^4\\) & & \\\\ \\hline (d) \\(g(x) = x^2 + 5x^{-9}\\) & & \\\\ \\hline \\end{tabular}$$

Explanation:

Analyze functions (a), (b), and (c)

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Analyze function (d)

$$ g(x) = x^2 + 5x^{-9} \implies \text{exponent } -9 otin \mathbb{N}_0 \implies \text{Not a Polynomial} $$

Answer:

Function	Is the function a polynomial?
(b) \(f(x) = 7x^7 + 9x^4 + \frac{x}{5}\)	Yes
(c) \(h(x) = 8x^9 + 0.9x^4\)	Yes
(d) \(g(x) = x^2 + 5x^{-9}\)	No