In these exercises, determine whether the equation represents y as a function of x.


19. \(y=\sqrt{x^2-1}\)

21. 2x+3y=4

23. y2=x2-1


I believe 19 and 23 are the same thing, am I correct or incorrect in said assumption?

rarinstraw1195  Sep 11, 2017

1+0 Answers


19.  y  = sqrt ( x^2 - 1)


This is the top half of a hyperbola


See the graph, here....https://www.desmos.com/calculator/cop6acsqup


Notice that this passes the vertical line test.. each x value is only associated with one y value...so it is a function


21.  2x + 3y  = 4   


This is the equation of a [nonvertical] line......this will always be a function


23 . y^2 = x^2 - 1


This graph is similar to 19, but is the complete hyperbola.....it does not pass the vertical line test because two different y's are associated with the same x value......[for instance.....if x = 2, y takes on the values  sqrt (2)  and - sqrt (2) ]


See the graph, here :  https://www.desmos.com/calculator/g13bkuiecg


Notice that the vertical line x = 2 cuts the graph in two places....



cool cool cool

CPhill  Sep 11, 2017

8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details