## Math4Life Group Title 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

1. mayankdevnani Group Title

option a

2. Math4Life Group Title

@mayankdevnani and how do you know that?

3. lgbasallote Group Title

look at the exponents on the right side...what exponents do you see?

4. lgbasallote Group Title

^by exponents i mean exponents of the variable/s

5. lgbasallote Group Title

i assume @Math4Life is currently offline.....

6. Math4Life Group Title

Sorry I was afk for 1 moment, im back though, sorry

7. lgbasallote Group Title

so what exponents do you see on the right side? (again i mean exponents of the variable/s)

8. Math4Life Group Title

x2 - 3

9. lgbasallote Group Title

just exponents...not the terms

10. Math4Life Group Title

x2 and 3?

11. lgbasallote Group Title

i think you are confused.... |dw:1350310291294:dw|

12. Math4Life Group Title

13. lgbasallote Group Title

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?

14. Math4Life Group Title

I got it so far

15. lgbasallote Group Title

good. now here comes the basic part. are 2 and 0 even, odd or neither?

16. Math4Life Group Title

even

17. lgbasallote Group Title

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?

18. Math4Life Group Title

Ya, i understand now, thanks!

19. lgbasallote Group Title

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 \[y = x^2 + x + 1\] \[y + x^3 + 1\] \[y + x^3 + x^2\]

20. lgbasallote Group Title

those last two parts should be \[y = x^3 + 1\] \[y = x^3 + x^2\]

21. lgbasallote Group Title

in case you get confused..you can refer to these examples

22. lgbasallote Group Title

by the way.. "both" means symmetric to origin

23. Math4Life Group Title

Thanks so much!

24. lgbasallote Group Title

welcome