Determine whether each equation is a function.

1. $4x+y=-3$
2. $x+y^2=1$
   
3. $y-x^2=2$

The equation is:

$4x+y=-3$

The above equation can be written as:

$y=-4x-3$

For each value of x, we multiply it by -4 and then subtract 3 to get the value of y.

Substitute $x=1$in $y=-4x-3$,

localid="1644631684346" $\begin{array}{rcl}y& =& -4\left(1\right)-3\\ & =& -4-3\\ & =& -7\end{array}$

It would work similarly for any value of x. Since each value of x corresponds to only one value of y the equation defines a function.

The equation is:

$x+y^2=1$

The above equation can be written as:

localid="1644629792440" $y^2=1-x$

Substitute $x=0$in the above equation,

$\begin{array}{rcl}{y}^2& =& 1-0\\ & =& 1\\ y& =& -1or1\end{array}$

It would work similarly for any value of x. Since each value of x does not correspond to only one value of y the equation does not define a function.

The equation is:

$y-x^2=2$

The above equation can be written as:

$y=2+x^2$

Substitute $x=1$in the above equation,

localid="1644631724375" $\begin{array}{rcl}y& =& 2+{\left(1\right)}^2\\ & =& 2+1\\ & =& 3\end{array}$

It would work similarly for any value of x. Since each value of x corresponds to only one value of y the equation defines a function.