In these exercises, determine whether the equation represents y as a function of x.
I believe 19 and 23 are the same thing, am I correct or incorrect in said assumption?
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....