Question

choose the function that represents the data in the table.
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$$\begin{tabular}{|c|c|c|c|c|c|c|} \\hline x & 0 & 1 & 2 & 3 & 4 & 5 \\\\ \\hline f(x) & -7 & 193 & 393 & 593 & 793 & 993 \\\\ \\hline \\end{tabular}$$

\\(f(x) = x^{200} - 7\\)
\\(f(x) = 200x - 7\\)
\\(f(x) = 200x^2 - 7\\)
\\(f(x) = 200^x - 7\\)

Explanation:

Find the y-intercept

$$ f(0) = -7 $$

Calculate the rate of change

$$ m = \frac{f(1) - f(0)}{1 - 0} = \frac{193 - (-7)}{1} = 200 $$

Formulate the linear function

$$ f(x) = 200x - 7 $$

Answer:

• \(f(x) = x^{200} - 7\)
• \(f(x) = 200x - 7\) (Correct answer)
• \(f(x) = 200x^2 - 7\)
• \(f(x) = 200^x - 7\)