SOLUTION: State whether or not the given equations determines y as a function of x 1. X+Y=1 2. X^2 + y^2=1 3. Y^2=X^2 4. Y=√x 5. Y=+-√X

Algebra ->  Functions -> SOLUTION: State whether or not the given equations determines y as a function of x 1. X+Y=1 2. X^2 + y^2=1 3. Y^2=X^2 4. Y=√x 5. Y=+-√X      Log On


   

Question 1207313: State whether or not the given equations determines y as a function of x
1. X+Y=1
2. X^2 + y^2=1
3. Y^2=X^2
4. Y=√x
5. Y=+-√X
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
State whether or not the given equations determines y as a function of x
1. x%2By=1
2.+x%5E2+%2B+y%5E2=1
3. y%5E2=x%5E2
4. y=sqrt%28x%29
5. +y+= +-sqrt%28x%29

use Vertical Line Test:
We use the vertical line test to determine whether the given equation is a function. This test says if every vertical line passes through maximum one point of the curve representing the equation, then the equation represents a function.
If the vertical line we drew passes through two points of the curve representing the equation, then the equation does not represents a function.

1. x%2By=1

=> equation is a function

2.+x%5E2+%2B+y%5E2=1

=>equation does not represents a function

3. y%5E2=x%5E2


=>equation does not represents a function

4. y=sqrt%28x%29

=>equation represents a function

5. +y+= +-sqrt%28x%29

=>equation does not represents a function


Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
State whether or not the given equations determines y as a function of x
(1) X+Y=1
(2) X^2 + y^2=1
(3) Y^2=X^2
(4) Y=√x
(5) Y=+-√X
~~~~~~~~~~~~~~~~~~~~~ 

(1)  From x + y = 1, we have an equivalent equation

         y = 1-x.

    It determines "y" by an unique way via x.  So, (1) determines "y" as a function of x.



(2)  From x%5E2 + y%5E2 = 1, we have an equivalent expression

         y = +/- sqrt%281-x%5E2%29.

    It determines two values of "y" for each value of x.  So, (2) does not determine "y" as a function of x.



(3)  From y%5E2 = x%5E2, we have an equivalent expression

         y = +/- |x|.

    It determines two values of "y" for each value of x.  So, (3) does not determine "y" as a function of x.



(4)  y = sqrt%28x%29  determines a unique value of "y" for each positive value of x.  

    So, (4) determines "y" as a function of x.



(5)  y = +/- sqrt%28x%29  determines two value of "y" for each positive value of x.  

    So, (5) does not determine "y" as a function of x.

Solved.

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