Determine whether x = 12 - y defines y as a function of x.

Question

i need help with finding or defining y as a function of x

Answer 1

y is a function of x if (and only if) each possible value of x can generate only one value of y.

Something like y = x^2 defines y as a function of x because, for any value of x you put in, there is only one possible value of y.

Something like y = sqrt(x) does not define y as a function of x because, for any positive value of x you put in, there are two possible values of y.  Example:  y = sqrt(x) when x = 4 gives us y = -2 and y = 2.

x = 12 - y

x + y = 12 - y + y

x + y = 12

x - x + y = 12 - x

y = 12 - x

This equation does define y as a function of x.  For each possible value of x, there is only one possible value of y.

If you want to visualze it, you might want to look up something called the 'vertical line test.'

Answer 2

x=12-y