Question 1206448: Which of the following relationships represents a function?
A.
(-5,0), (5,3), (-7,1), (5,5)
B.
(-5,4), (5,6), (-5,3), (2,2)
C.
(-5,4), (4,6), (-5,3), (1,2)
D.
(-5,5), (5,3), (-7,2), (2,3)
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
A relationship is NOT a function if there are any cases where a given x value has two different y values.
A.
(-5,0), (5,3), (-7,1), (5,5)
x=5 has two different y values, 3 and 5 --> NOT a function
B.
(-5,4), (5,6), (-5,3), (2,2)
x=-5 has two different y values, 4 and 3 --> NOT a function
C.
(-5,4), (4,6), (-5,3), (1,2)
x=-5 has two different y values, 4 and 3 --> NOT a function
D.
(-5,5), (5,3), (-7,2), (2,3)
All the x values are different, so there is no way that there can be two different y values for any x value. This is a function.
ANSWER: D
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Answer: Choice D
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
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
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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