Consider y = −√x. Is y a function of x? Why or why not? Is it true that |y| is always less than x? Show that it is or give a counter example.

Question

Consider y = −√x. Is y a function of x? Why or why not? Is it true that |y| is always less than x? Show that it is or give a counter example.

Answer 1

y = -√x is a function since the graph passes the Vertical Line Test.

It is not the case that l y l < x always. For instance, if x = 1/4, then l y l = 1/2. So, l y l > x.