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# Determine whether y is a function of x

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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
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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

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