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The standard form of an inverse proportional function is:

$\mathrm{f(x)}=\frac{a}{x}$

When a function is inversely proportional, it means that the x values and the values along the y-axis (e.g., f(x)) respond oppositely to each other.

In an inverse proportional relationship:

• When the x value doubles, the f(x) value is halved.
• When the x value halves, the f(x) value is doubled.
• When the f(x) value doubles, the x value is halved.
• When the f(x) value halves, the x value is doubled.
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Note:
In a directly proportional function, when moving from x = 1 to x = 2, the y-value changes from 2 to 4, meaning the y-value doubles as the x-value doubles.

In an inversely proportional function, when moving from x = 1 to x = 2, the y-value changes from 2 to 1, meaning the y-value is halved as the x-value doubles.