+0  
 
+1
558
1
avatar+5250 

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
avatar+88980 
+4

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

9 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.