Question

Is `f(x) =x^4sqrt(5-x)` a function?

Answer 1

Yes, it is. Given any value of `x` we never get two values for `f(x)` (We sometimes get no value, but that has to do with the domain, not with being a function.)

This was posted under "Vertical Line Test" which requires a graph. Using graphing technology, here is the graph:

graph{y=x^4sqrt(5-x) [-27.3, 37.68, -4.73, 27.74]}

It is hard to see the graph, and scrolling out makes it look weird.

Here's a similar graph with the scale changed so that each `1` on the `y`-axis represents 100: (I divided the function by 100.)

graph{y=(x^4sqrt(5-x))/100 [-18.8, 21.77, -2.49, 17.79]}

It is fairly clear that this graph passes the vertical line test.

(It is also fairly clear that the domain is `x <= 5`)