Question

Determine whether each equation is a function.

1. $x+y^2=4$
2. $y=x^2-7$
3. $y=5x-4$

Short answer

Part (a) $x+y^2=4$is not a function.

Part (b) $y=x^2-7$is a function.

Part (c) $y=5x-4$is a function.

Step-by-step solution

Part (a) Step 1.

The equation is:

$x+y^2=4$

The above equation can be written as:

$y^2=4-x$

Substitute $x=0$in the above equation,

$\begin{array}{rcl}{y}^2& =& 4-0\\ & =& 4\\ y& =& 2or-2\end{array}$

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.

Part (b) Step 1.

The equation is:

$y=x^2-7$

Substitute $x=0$in the above equation,

$\begin{array}{rcl}y& =& {\left(0\right)}^2-7\\ & =& 0-7\\ & =& -7\end{array}$

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.

Part (c) Step 1.

The equation is:

$y=5x-4$

Substitute $x=0$in the above equation,

$\begin{array}{rcl}y& =& 5\left(0\right)-4\\ & =& 0-4\\ & =& -4\end{array}$

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.