determine whether the equation defines y as a function of x.
√x + y = 12
y = 12-√x
looks like a function to me, though the domain is restricted.
To determine whether the equation defines y as a function of x, we need to see if for every value of x, there is a unique value of y.
First, let's rearrange the equation to isolate y:
√x + y = 12
Subtracting √x from both sides:
y = 12 - √x
Now, we can see that y is indeed defined as a function of x because for every value of x, there is only one corresponding value of y. Each value of x will produce a unique value of y.
Therefore, the equation √x + y = 12 defines y as a function of x.