DIRECTIONS :

Variation is a great example of how mathematics is used to model and solve real-world problems. Many fields of study contain examples of the three different kinds of variation:

Direct variation (for example, y = kx)
Inverse variation (for example, y = k/x)
Joint variation (for example, z = kxy)
Definition of Joint Variation

Joint variation is the same as direct variation with two or more quantities.

That is:

Joint variation is a variation where a quantity varies directly as the product of two or more other quantities.

Let's first understand direct variation.

Direct variation occurs when two quantities change in the same manner.

That is:

Increase in one quantity causes an increase in the other quantity.

Decrease in one quantity causes a decrease in the other quantity.

For example:

The cost of a pencil and the number of pencils you buy.

Buy more pay more….Buy less pay less.

Direct variation between variables x and y can be expressed as:

y = kx, where 'k' is the constant of variation and k ≠ 0.

y = kxz represents joint variation. Here, y varies jointly as x and z.

More Examples on Joint Variation
y = 7xz, here y varies jointly as x and z.
y = 7x2z3, here y varies jointly as x2 and z3."
for example, a biker traveling at 8 mph can cover 8 miles in 1 hour. If the biker's speed decreases to 4 mph, it will take the biker 2 hours (an increase of one hour), to cover the same distance.

QUESTION : Give an example from real life where composite functions are utilized. For ideas, you may look it up on the internet or find examples in the book