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

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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)   (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.
2.
3.
4.
5. = +-

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.

=> equation is a function

2.

=>equation does not represents a function

3.


=>equation does not represents a function

4.

=>equation represents a function

5. = +-

=>equation does not represents a function


Answer by ikleyn(52798)   (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  +  = 1, we have an equivalent expression

         y = +/- .

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



(3)  From  = , 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 =   determines a unique value of "y" for each positive value of x.  

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



(5)  y = +/-   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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