Algebra 2 Question, help?

Question

Please help it's a new class and i'm already a bit confused on this question.

It asks:

Why does y=3 represent a function, but x=3 does not?

Answer 1

By definition, a function can only have one y-value for any given x-value.  A visual way to test this: if you can draw a vertical line anywhere and it intersects the graph more than once, it is not a function. If it intersects at most once, it is a function.

In the case of x = 3, the graph is a vertical line, and applying the test given above, a vertical line can intersect the graph in more than one point (in fact, infinitely many points). Thus, it is not a function.

For y = 3, the graph is a horizontal line. A vertical line can only intersect it at a single point no mater where you put it, so it is a function.

To look at it algebraically, if points (a, b) and (a, c) are both on the graph, it is not a function, since the same x-value has two different y-values.

Answer 2

A function can only have one X value at each point. However, what you are talking about is Y(X) or function of X.

In X(Y) or function of Y the x = 3 would be correct. In this case there can only be one Y value at each point.