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

$y=-\frac{1}{9}x$

$y=8x$

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

$y=\frac{6-x}{3}$

$x=2y^2-3$

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

$y^2=\frac{x+3}{2}$

To find y we will take square root for both sides

$\begin{gathered} \sqrt[]{y^2}=\pm\sqrt[]{\frac{x+3}{2}} \\ y=\pm\sqrt[]{\frac{x+3}{2}} \end{gathered}$

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

This can not be a function