Question

which type of function best models the data in the table below?

\\(\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline 2 & 4 \\\\\\hline 4 & 2 \\\\\\hline 6 & 1\\frac{1}{3} \\\\\\hline 8 & 1 \\\\\\hline 10 & \\frac{4}{5} \\\\\\hline\\end{array}$$

\\)

• inverse variation
• linear
• logarithmic
• quadratic

Explanation:

Calculate the product of x and y for each data point

$$
LATEXBLOCK0
$$

Identify the constant product relationship

$$ x \cdot y = 8 \implies y = \frac{8}{x} $$

Determine the matching function type

$$ y = \frac{k}{x} \quad (\text{Inverse Variation}) $$

Answer:

• inverse variation (Correct answer)
• linear
• logarithmic
• quadratic