Inversely proportional function
An inversely proportional function is a function of the form:
where k is the proportionality constant, and x ≠ 0.
The graph of an inversely proportional function is called a hyperbola (see the figure to the right).
If you rewrite the formula for an inversely proportional function, you can see that if x and y are multiplied together, you will always get the same number, which is the constant k:
So if you have two sets of data, and you want to know if their relationship is inversely proportional, you simply just need to multiply each pair of x- and y-values. If all of these products are the same number, it’s an inversely proportional function.
How does the proportionality constant k affect the function’s graph?
The closer to 0 k is, the closer to the point (0,0) the graph is.
k > 0: If x is positive, y is also positive. If x is negative, y is also negative.
k < 0: If x is positive, y is negative. If x is negative, y is positive.