Recall the definition of a function and the tests to check if a relation is a function.
Yes, see solution.
Practice makes perfect
We are asked if a function can have an infinite number of values in its domain while having a finite number of values in its range.
This is not only possible but, there are infinitely many solutions. Here, we will only illustrate one example. Let's use a horizontal line and the vertical line test.
In the example shown above, at any point along the x-axis, a vertical line would only pass through the graph at one point. Therefore, a horizontal line is a valid function. Notice that horizontal lines have an infinite number values in their domain but only one value in their range. For our example, we have the following.
Domain:& - ∞ < x < ∞
Range:& 2
A horizontal line can help us model things that never change.
Real World Example
Continuing with the same function as shown above, a real-world example using this function could be the number of planets closer to the sun than the Earth.
Let x be time relative to now, now being x=0, and let y be the number of planets closer to the sun. No matter what point in time we go back or forward to (ignoring any gigantic future planet-destroying or adding catastrophes), there will always be 2 planets closer to the sun, Mercury and Venus.
