For questions a - b, tell whether the set of ordered pairs (x, y) defined by each equation is a function.
(a) y = x^3 - 3x
(b) y = + - sqrt{1 - 2x}
(c) x + 2y^2 = 1
How can I tell simply by looking at each equation?
I wouldn't look at the equation, I'd look at the graph. Do you know what the "vertical line test" is?
Graph each function. If, when you pass a vertical line through any portion of the graph, the line intersects your function in at most one point, the graph defines a function.
We can easily see the b and c are not functions, whereas a is.
-Dan