Question

Determine whether the equation defines y as a function of x. x+y=9 and x^2+y^2=1 and x=y^2

Answer 1

Answer:

Function: $x+y=9$

Not Function: $x^2+y^2=1$    and     $x=y^2$

Step-by-step explanation:

Given

$x+y=9$

$x^2+y^2=1$

$x=y^2$

Required

Determine if $y$ is a function of $x$

Solving x+y=9

$x+y=9$

Make y the subject of formula

$y = 9 - x$

Hence; y is a function of x

Solving $x^2+y^2=1$

$x^2+y^2=1$

Subtract x² from both sides

$y^2=1 - x^2$

Square root of both sides

$y =\± \sqrt{1 - x^2}$

This implies that

$y =\sqrt{1 - x^2}$     or     $y =-\sqrt{1 - x^2}$

Because $y$ can be any of those two expressions, it is not a function.

Solving $x=y^2$

$x=y^2$

Reorder

$y^2 = x$

Take square roots

$y = \±\sqrt{x}$

This implies that

$y = \sqrt{x}$      or        $y = -\sqrt{x}$

Because $y$ can be any of those two expressions, it is not a function.