Question

choose the function that represents the data in the table.

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$$\begin{array}{|c|c|c|c|c|c|c|} \\hline x & 0 & 1 & 2 & 3 & 4 & 5 \\\\ \\hline f(x) & -3 & -1 & 1 & 3 & 5 & 7 \\\\ \\hline \\end{array}$$

\\(f(x) = \frac{2}{x} - 3\\)

\\(f(x) = 2x - 3\\)

\\(f(x) = x^2 - 3\\)

\\(f(x) = 2x^2 - 3\\)

Explanation:

Determine the rate of change

$$ m = \frac{f(1) - f(0)}{1 - 0} = \frac{-1 - (-3)}{1} = 2 $$

Find the y-intercept

$$ b = f(0) = -3 $$

Formulate the linear function

$$ f(x) = 2x - 3 $$

Answer:

• \(f(x) = \frac{2}{x} - 3\)
• \(f(x) = 2x - 3\) (Correct answer)
• \(f(x) = x^2 - 3\)
• \(f(x) = 2x^2 - 3\)