Question 85189: 1. Determine if each of the following is a relation or a function. Tell me why and give me the domain and range of each one.
a. (0,1) (4,1) (6,2) (2,0)
b. (1,2) (3,1) (1,3) (2,0)
c. y = 5
d. y = 6 _
2x -1
e. note that these curves extend to infinity at each
end.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! a.
Plot the 1st point (0,1)
Plot the 2nd point (4,1)
Plot the 3rd point (6,2)
Plot the 4th point (2,0)
Now connect these points with a crude line (it doesn't matter at this point)
Since this graph passes the vertical line test, this relation is a function. Here we can see the domain (the set of allowable x values) is {0,4,6,2} and the range (the set of y values) is {1,1,2,0}
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b.
Plot the 1st point (1,2)
Plot the 2nd point (3,1)
Plot the 3rd point (1,3)
Plot the 4th point (2,0)
Again, draw an approximate "curve" through all of the points
Since we can clearly see that the graph fails the vertical line test, this relation is not a function.
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c.
graph this relation
Since this graph passes the vertical line test, this relation is a function. Here we can see the domain is x can be any number and the range is 5
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d.
graph this relation
Since this graph passes the vertical line test, this relation is a function. Here we can see the domain is x can be any number, except x cannot equal  and the range is y can be any number, except y cannot equal 
So to recap, the only relation that isn't a function is choice b)
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