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

1 Answer
May 19, 2015

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#)