SOLUTION: Determine if each of the following is a relation or a function. Tell why and give the domain and range of each one. a) (0,1)(4,1)(6,2)(2,0) b) y=6 over 2x-1

Question 52654: Determine if each of the following is a relation or a function. Tell why and give the domain and range of each one.
a) (0,1)(4,1)(6,2)(2,0)
b) y=6 over 2x-1
Found 2 solutions by funmath, venugopalramana:
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
a) (0,1), (4,1), (6,2), (2,0)
This is a function because for every x there is exactly one y. Y's can have more than one x, but x's can have only one y.
The Domain corresponds with the x values is {0,4,6,2}, the range corresponds with the y values is {1,1,2,0}
b) y=6/(2x-1)
This is a function. When dealing with equations it is often easiest to look at y. If it's not raised to an even power it's a function.
For rational (fractions with variables in the denominator) functions the domain can be found by finding out what makes the denominator =0 (thus be undefined)
2x-1=0
2x-1+1=0+1
2x=1
2x/2=1/2
x cannot = 1/2
Set builder notation:{x|x cannot=1/2}
Interval notation: (- infinity, 1/2)U(1/2,+infinity)
For the Range: y cannot eqaul 0.
Set builder notation:{y|y cannot=0}
Interval:(-infinity,0)U(0,+infinity)
I don't know what math you're taking, so I don't want to tell you too much about how I know the range and freak you out. Resubmit that portion with the level of math you're in and I'll tell you how to find out that y cannot = 0. If you're in algebra, you can probably just plug it into your graphing calculator and look at what y can't be. If your in precal or calculus, take the limit as x approaches infinity.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Determine if each of the following is a relation or a function. Tell why and give the domain and range of each one.
a) (0,1)(4,1)(6,2)(2,0).
each first member has a unique image.hence it is a function
domain is 0,4,6,2
range is 1,2,0
b) y=6 over 2x-1
y=6/(2x-1)
each x has a unique image.hence it is function.
domain is all real numbers except x=0.5 since in such a case it would result in division by zero which has no meaning.
range is all real numbers except 0,since y canot be zero for any finite value of x
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