91Ó°ÊÓ

$y=3x-5$

For each value of $x$, we multiply it by $3$and then subtract $5$to get the value of $y$.

Substitute $x=1$in $y=3x-5$,

localid="1644817848638" $\begin{array}{rcl}y& =& 3\left(1\right)-5\\ & =& 3-5\\ & =& -2\end{array}$

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.

$y=x^3$

For each value of $x$, cube it to get the value of $y$.

Substitute $x=1$in $y=x^3$,

localid="1644817931186" $\begin{array}{rcl}y& =& {\left(1\right)}^3\\ & =& 1\end{array}$

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.

$2x+y^2=4$

The above equation can be written as:

$y^2=4-2x$

Substitute $x=0$in the above equation,

localid="1644818020959" $\begin{array}{rcl}{y}^2& =& 4-2\left(0\right)\\ & =& 4-0\\ & =& 4\\ y& =& -2or2\end{array}$

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.