An inverse proportion function is a mathematical relationship where two variables have a constant product. The general form is y equals k over x, where k is a non-zero constant. As x increases, y decreases proportionally, creating a hyperbolic curve. This relationship appears frequently in physics and real-world applications.
The mathematical form of an inverse proportion function is y equals k over x, where k is a non-zero constant. The domain excludes x equals zero since division by zero is undefined. A key property is that the product of x and y always equals the constant k. The graph consists of two branches - one in the first quadrant and one in the third quadrant when k is positive.
The constant k determines the shape and position of the hyperbola. When k is positive, the graph appears in the first and third quadrants. When k is negative, it appears in the second and fourth quadrants. The larger the absolute value of k, the farther the curve is from the origin. All inverse proportion functions have asymptotes at the x and y axes.
Inverse proportion functions appear frequently in real-world situations. In physics, Boyle's Law states that pressure times volume equals a constant for a gas at constant temperature. In economics, there's often an inverse relationship between price and quantity demanded. A common example is travel: if you need to cover 24 kilometers, your speed and time are inversely proportional - doubling your speed halves the time needed.