Question 145375: Please help me solve this question. Which of the following relations is (are) functions?
a. {(x,y)| y^2=2x+1}
b. {(x,y)| y=2x^2+1}
c. {(2,3), (3,3), (4,3)}
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! For each of the given functions, ask "Can I find a value of the independent variable, x in this case, that maps to more than 1 value of the dependent variable, y?" If you cannot, then you have a function. But if any value of x yields more than 1 possible value for y, then you do not have a function.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Please help me solve this question. Which of the following relations is (are) functions?
a. {(x,y)| y^2=2x+1}
Solve for "x" : x = (y^2-1)/2
This is a parabola opening to the right.
It is not a function.
Notice that when x = 0, y^2 = 1, so y could be +1 or it could be -1.
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b. {(x,y)| y=2x^2+1}
This is a prabola opeing up and is a function.
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c. {(2,3), (3,3), (4,3)}
Each different x value has a unique y-value paired with it.
It is a function.
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Cheers,
Stan H.
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