**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.** y^{2}=x^{2}-1

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

rarinstraw1195
Sep 11, 2017

#1**+2 **

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....

CPhill
Sep 11, 2017