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Math4Life

The graph of the equation y = x2 – 3 is symmetric with respect to which of the following? A. the x–axis B. the y–axis C. the origin D. none of these

  • one year ago
  • one year ago

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  1. mayankdevnani
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    option a

    • one year ago
  2. Math4Life
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    @mayankdevnani and how do you know that?

    • one year ago
  3. lgbasallote
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    look at the exponents on the right side...what exponents do you see?

    • one year ago
  4. lgbasallote
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    ^by exponents i mean exponents of the variable/s

    • one year ago
  5. lgbasallote
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    i assume @Math4Life is currently offline.....

    • one year ago
  6. Math4Life
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    Sorry I was afk for 1 moment, im back though, sorry

    • one year ago
  7. lgbasallote
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    so what exponents do you see on the right side? (again i mean exponents of the variable/s)

    • one year ago
  8. Math4Life
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    x2 - 3

    • one year ago
  9. lgbasallote
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    just exponents...not the terms

    • one year ago
  10. Math4Life
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    x2 and 3?

    • one year ago
  11. lgbasallote
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    i think you are confused.... |dw:1350310291294:dw|

    • one year ago
  12. Math4Life
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    oops my bad, so ^2

    • one year ago
  13. lgbasallote
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    close.... remember this: when you have a constant (which are whole numbers without variables) the exponent of their variable is 0 so the exponents of the variables here are 2 and 0 got it?

    • one year ago
  14. Math4Life
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    I got it so far

    • one year ago
  15. lgbasallote
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    good. now here comes the basic part. are 2 and 0 even, odd or neither?

    • one year ago
  16. Math4Life
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    even

    • one year ago
  17. lgbasallote
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    good. now, when *all* the exponents of the variables *on the right side* are even, then it is automatically symmetric to the y-axis. if the exponents of the variables *on the right side* are *all* odd, then it is symmetric to the y-axis. if the exponents of the left side and right side have the same parity (parity means that the exponents of the left side and right side are either BOTH odd or BOTH even), then it is symmetric to the origin. If neither, then neither. did you follow that?

    • one year ago
  18. Math4Life
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    Ya, i understand now, thanks!

    • one year ago
  19. lgbasallote
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    here are some examples to guide you: even function: \[y = x^4 + x^2 + 3\] \[y = x^2\] \[y = 3\] odd function \[y= x^3 + x\] \[y = x^5 + x\] \[y = x^5 + x^3 + x\] both \[y = x\] \[y^2 = x^2\] \[y^3 = x^5 + x^3\] neither \[y = x^2 + x + 1\] \[y + x^3 + 1\] \[y + x^3 + x^2\]

    • one year ago
  20. lgbasallote
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    those last two parts should be \[y = x^3 + 1\] \[y = x^3 + x^2\]

    • one year ago
  21. lgbasallote
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    in case you get confused..you can refer to these examples

    • one year ago
  22. lgbasallote
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    by the way.. "both" means symmetric to origin

    • one year ago
  23. Math4Life
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    Thanks so much!

    • one year ago
  24. lgbasallote
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    welcome

    • one year ago
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