Question

For each equation determines whether y is a funcation of x

Answer 1

All linear relations are functions

The quadratic equations can be a function if we restrict the domain of it

The given relations are

`x=-9y`

This is a linear relation, then it is a function, we can put it in the form

`y=-(1)/(9)x`

`y=8x`

This is a linear relation, then it is a function

`x+3y=6`

This is a linear relation, then it is a function, we can put it in the form

`y=(6-x)/(3)`

`x=2y^2-3`

We will put it in the form of y as a subject

`y^2=(x+3)/(2)`

To find y we will take square root for both sides

`\begin{gathered} \sqrt[]{y^2}=\pm\sqrt[]{(x+3)/(2)} \\ y=\pm\sqrt[]{(x+3)/(2)} \end{gathered}`

That means each value of x has 2 values of y, then

This can not be a function