Which of these are not functions?

Question

dtan5457 · Answer

attachment

dtan5457 · Answer

someone refresh me on what those dots are..

danjs · Answer

THe open dot means , the point is less than or greater than, it doesnt include the point

danjs · Answer

For each x value, there can only be one Y value for each to be a function.

danjs · Answer

Scan a Vertical Line across the graphs, which one intersects the vertical line more than once at a single x value?

danjs · Answer

For sure graph (1) is a function , by those rules

dtan5457 · Answer

So a closed dot, means that its included, right?

danjs · Answer

What about 2?

danjs · Answer

yeah closed dot means it includes the point

danjs · Answer

open dot means it can be arbitrarily close to that point, but not = to it

dtan5457 · Answer

Then it appears to be 3. what does 2 mean though?

dtan5457 · Answer

doesn't it fail the vertical line test?

danjs · Answer

Right, (3) is the one that fails, and is not a function...

danjs · Answer

Graph 2, looks like the graph of Y= Tan(x)

danjs · Answer

Where do you see a vertical line crossing the graph more than once on there?

danjs · Answer

There are values where the graph is undefined, where they shoot off to infinity, but that doesnt make it not a function.

dtan5457 · Answer

we didn't learn tan functions in trig yet. i see now, i thought one line of each tan had to pass the test

danjs · Answer

Like Tan(pi/2) or tan(90)

danjs · Answer

the tangent is the opposite side of a triangle over the adjacent side of the angle in a triangle

danjs · Answer

at 90 degrees on a unit circle, the x value is zero, so y/x = y/0  
zero in the denominator is undefined, as you get close to x=90 degrees, the tangent shoots off towards infinity

danjs · Answer

That is what you see on graph(2)

danjs · Answer

every interval of 90 or pi/2

danjs · Answer

It looks as though that graph has vertical lines and would fail, but those really arent vertical, they are getting ever closer to vertical, but never reaching it

danjs · Answer

Just as what happens at the Y-axis in Graph(1)

danjs · Answer

In case you want to mess around with them: 
Graph 1 looks like- y =1/x 
Graph 2 looks like- y=tan(x)
Graph 3 - Not a function
Graph 4 - step function