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

Function:

Not Function:    and    

Step-by-step explanation:

Given

Required

Determine if is a function of

Solving x+y=9

Make y the subject of formula

Hence; y is a function of x

Solving

Subtract x² from both sides

Square root of both sides

This implies that

    or    

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

Solving

Reorder

Take square roots

This implies that

     or        

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

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.