Question

I need help!
Reasoning: Can a function have an infinite number of values in its domain and only a finite number of values in its range? If so, describe a real-world situation that could be modeled by such a function.

Writing: What is the difference between a relation and a function? Is every relation a function? Is every function a relation? Explain.

Answer 1

Sure. Consider a step function.
[x] is the greatest integer less than or equal to x.

For example,

[1.3] = 1
[1.9] = 1

Now consider the domain as the interval [1,2]

The domain is the whole interval, with infinitely many values, but the range is a single value: y=1

Such a step function could describe the position of a ratchet on a gear. The angle varies continuously, but the ratchet assumes only a finite number of positions.

A relation is just a set of value pairs, relating each first value to the second value.

The relation is a function only if no two first-values are related to the same second-value.