anonymous
  • anonymous
are parabolas that open to the right / left quadratic functions too?
Mathematics
schrodinger
  • schrodinger
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UnkleRhaukus
  • UnkleRhaukus
parabolas that open to the left are right are not functions, they are relations
UnkleRhaukus
  • UnkleRhaukus
a function can only have a single output for the each input a test for this is the vertical line test, which say that on the graph of a relation, if any vertical line touches the line of the relation at more than one place the the relation is not a function |dw:1356789558553:dw|
anonymous
  • anonymous
THANK YOU, SO MUCH! ;D

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UnkleRhaukus
  • UnkleRhaukus
i would say that \(x=y^2\) is a quadratic relation though
UnkleRhaukus
  • UnkleRhaukus
kinda similar is \[y=\sqrt x\] |dw:1356789914537:dw| which only has one output for each input and thus passes the vertical line test so \[y=\sqrt x\] is a function
UnkleRhaukus
  • UnkleRhaukus
These relations are different so you'll have to remember to be carful if you want to rearrange the first relation \[y^2=x\]\[y=+\sqrt x,-\sqrt x\]\[\quad=±\sqrt x\] which is clearly not a function as it has two values for most inputs

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