Question

in a function, \\(y\\) varies inversely with \\(x\\). the constant of variation is 4. which table could represent the function?

Explanation:

Set up the inverse variation equation

$$ y = \frac{k}{x} \implies xy = k $$

$$ xy = 4 $$

Test the given tables

• Table 1 (top-left):

$$ (-2)(-8) = 16 e 4 $$

• Table 2 (top-middle):

$$ (-2)(-2) = 4,\quad (-1)(-4) = 4,\quad (1)(4) = 4,\quad (2)(2) = 4 $$

• Table 3 (top-right):

$$ (-2)(2) = -4 e 4 $$

• Table 4 (bottom-left):

$$ (-2)(4) = -8 e 4 $$

Identify the correct table

The second table (top-middle) satisfies \(xy = 4\) for all pairs.

Answer:

• (A) Table with pairs (-2, -8), (-1, -4), (1, 4), (2, 8)
• (B) Table with pairs (-2, -2), (-1, -4), (1, 4), (2, 2) (Correct answer)
• (C) Table with pairs (-2, 2), (-1, 4), (1, 4), (2, 2)
• (D) Table with pairs (-2, 4), (-1, 2), ...