Question

Use algebraic means to show that x^2 + y^2 = 8 is not a function. Explain your process.

Answer 1

For a single value of x function has more than one corresponding value of y which satisfies the equation.

Explanation:

Function: A relationship between a set of inputs and a set of possible outputs, where exactly one output is associated with each input.

It means for an equation to represent a function any single value of x there should be only one corresponding value of y which satisfies the equation.

Now consider the given equation.

`x^2 + y^2 = 8`

If we put x=0 then we get two value of y i.e
`\sqrt8` and
`-\sqrt8` which satisfy the equation and therefore the equation is not a function.