Determine whether the following equation defines y as a function of x. x squared plus yequals100 does the equation x squared plus yequals100 define y as a function of x?

It sounds like if you want to know if x^2+y = 100 is a function of x. Since we can isolate y to get y = -x^2+100, this means we have a function in terms of x. In other words, y is a function of x. Pick any number you want for x, plug it in for x and evaluate. You'll get exactly one output. The fact that we get exactly one output means that we have a function. 

In a visual sense, graphing the given equation produces what you see in the attached image. Note how it's impossible to draw a vertical line through more than one point on the red curve. Therefore, this graph passes the vertical line test and it means we have a function. 

Side Note: this curve is called a parabola