Question 1206448
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Answer: <font color=red>Choice D</font>


Reason: The x values don't repeat in choice D.

 
Something like choice A has x = 5 repeating itself.
That means x = 5 maps to more than one y output (y = 3 and y = 5), and why we don't have a function for choice A.
Choices B and C are a similar story.
The y values can repeat, but the function wouldn't be one-to-one (aka injective). Choice D is not injective since y = 3 repeats itself.


You can use the vertical line test to visually confirm if you have a function or not. 
If it is possible to draw a single vertical line through more than one point, then it's not a function.


Let's plot the points for Choice A
{{{
drawing(400,400,-10,10,-10,10,
graph(400,400,-10,10,-10,10),
circle(-5,0,0.05),circle(-5,0,0.07),circle(-5,0,0.09),circle(-5,0,0.11),circle(-5,0,0.13),circle(-5,0,0.15),circle(5,3,0.05),circle(5,3,0.07),circle(5,3,0.09),circle(5,3,0.11),circle(5,3,0.13),circle(5,3,0.15),circle(-7,1,0.05),circle(-7,1,0.07),circle(-7,1,0.09),circle(-7,1,0.11),circle(-7,1,0.13),circle(-7,1,0.15),circle(5,5,0.05),circle(5,5,0.07),circle(5,5,0.09),circle(5,5,0.11),circle(5,5,0.13),circle(5,5,0.15)
)
}}}
The two points on the right tell us that choice A fails the vertical line test.
So it is not a function.
Choice B and choice C will produce graphs that have a similar feature.


In contrast choice D looks like this
{{{
drawing(400,400,-10,10,-10,10,
graph(400,400,-10,10,-10,10),
circle(-5,5,0.05),circle(-5,5,0.07),circle(-5,5,0.09),circle(-5,5,0.11),circle(-5,5,0.13),circle(-5,5,0.15),circle(5,3,0.05),circle(5,3,0.07),circle(5,3,0.09),circle(5,3,0.11),circle(5,3,0.13),circle(5,3,0.15),circle(-7,2,0.05),circle(-7,2,0.07),circle(-7,2,0.09),circle(-7,2,0.11),circle(-7,2,0.13),circle(-7,2,0.15),circle(2,3,0.05),circle(2,3,0.07),circle(2,3,0.09),circle(2,3,0.11),circle(2,3,0.13),circle(2,3,0.15)
)
}}}
in which it is impossible to draw a single straight vertical line through more than one point. Therefore, choice D passes the vertical line test and it is a function.
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