Question

Which set of points represents a function?
A. (-5, -4), (-4,-3), (-3, -2), (-2, -1)
B. (-6,2), (6,-2), (-5, 3), (-5,-3)
C. (8, -1), (8,2), (8,-3), (8,4)
D. (1,3), (-4,4), (3,-2), (1,0)

Can someone please tell me how they got the answer? Thanks

Answer 1

for a set of ordered pairs, a function will have no x-repeats, namely, the x-coordinate in the pairs, do not repeat, they're unique.

now if the set has one x-repeat, then is NOT a function, let's check these ones,

$\bf A.\qquad (-5, -4), (-4,-3), (-3, -2), (-2, -1)\\\\ B.\qquad (-6,2), (6,-2), (\stackrel{\stackrel{rep eat}{\downarrow }}{-5}, 3), (\stackrel{\stackrel{rep eat}{\downarrow }}{-5},-3)$

$\bf C.\qquad (\stackrel{\stackrel{rep eat}{\downarrow }}{8}, -1), (\stackrel{\stackrel{rep eat}{\downarrow }}{8},2), (\stackrel{\stackrel{rep eat}{\downarrow }}{8},-3), (\stackrel{\stackrel{rep eat}{\downarrow }}{8},4)\\\\ D.\qquad (\stackrel{\stackrel{rep eat}{\downarrow }}{1},3), (-4,4), (3,-2), (\stackrel{\stackrel{rep eat}{\downarrow }}{1},0)$

so, the ones with a repeated x-value, are not functions.

Answer 2

Set A is a functions.

(B) is not it because there are two -5 for the x  and the -5 goes to 3 and -3. You cannot have the x value point to two different y values.

(C) The same thing for C but the x value is 8, which 8 points to different values.

(D) Yep, this goes for D too. There are two 1 for x and the 1 has two different 1 values,