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=sqrt(x)}}}
5. {{{ y }}}= +-{{{sqrt(x)}}}


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+y=1}}}

{{{ drawing( 600, 600, -10, 10, -10, 10,
green(line(3,10,3,-10)),
graph( 600, 600, -10, 10, -10, 10, -x+1)) }}}

=> equation is a function


2.{{{ x^2 + y^2=1}}}

{{{ drawing( 600, 600, -10, 10, -10, 10,
green(line(0.5,10,0.5,-10)),
graph( 600, 600, -10, 10, -10, 10, sqrt(-x^2+1),-sqrt(-x^2+1))) }}}

 =>equation does not represents a function


3. {{{y^2=x^2}}}


{{{ drawing( 600, 600, -10, 10, -10, 10,
green(line(3,10,3,-10)),
graph( 600, 600, -10, 10, -10, 10, sqrt(x^2),-sqrt(x^2))) }}}

 =>equation does not represents a function


4. {{{y=sqrt(x)}}}

{{{ drawing( 600, 600, -10, 10, -10, 10,
green(line(3,10,3,-10)),
graph( 600, 600, -10, 10, -10, 10, sqrt(x)))) }}}

 =>equation represents a function


5. {{{ y }}}= +-{{{sqrt(x)}}}

{{{ drawing( 600, 600, -10, 10, -10, 10,
green(line(3,10,3,-10)),
graph( 600, 600, -10, 10, -10, 10, sqrt(x),-sqrt(x))) }}}

 =>equation does not represents a function