Answer:
I. Not a function
II. Not a function
III. Yes, function
IIII. Yep!
(I messed up the numbering in the explanations, sorry 3 is 4 and 4 is 3)
Explanation:
Hi!
For a function, every x value must have exactly 1 y value.
f(2) can't equal both 0 and 10. It can only equal 0 or 10. So, because of this, we have a test called the vertical line test. Basically, you drag a line through a graph, and if there is any x value that goes to two (or more) different y-values, then that graph is not the graph of the function.
Let me try to give a practical explanation.
I.
In this graph, everything looks fine until we reach x=6. (I'm assuming the graph goes by ones). Do you see the problem? Yep! x has two different y values.
y= 4 and y= 6.
So, this isn't a function. Why? Because there are two y values for each x value (aka, this doesn't pass the V.L.T)
II.
(1,2), (2,5) , (3,8) , (2,-5) (1,-2)
We have two groups of problem points.
(2,5) and (2,-5) and (1,2) and (1,-2)
Here, each x value goes to a different y value. Therefore, this isn't a function
III. y=x^2
This is your typical parabola. See the graph that I attached.
Notice that -2 and 2 both go to 4. Two different x-values going to the same y-value is fine, but one x can't go to to different y values.
IIII.
(-4,1) , (0,3) , (4,5) , (6,6)
Check 1: Does any x-value go to multiple y values? Nope! So, this is a function.