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Unformatted text preview: equation doesn’t have symmetry
about the x-axis.
Next, let’s check symmetry about the y-axis. Here we’ll replace all x’s with –x. y = (-x) - 6( -x) + 2
2 4 y = x2 - 6 x4 + 2
After simplifying we got exactly the same equation back out which means that the two are
equivalent. Therefore, this equation does have symmetry about the y-axis.
Finally, we need to check for symmetry about the origin. Here we replace both variables. - y = (-x) - 6 (-x) + 2
2 4 - y = x2 - 6 x4 + 2
So, as with the first test, the left side is different from the original equation and the right side is
identical to the original equation. Therefore, this isn’t equivalent to the original equation and we
don’t have symmetry about the origin.
[Return to Problems] (b) y = 2 x 3 - x5
We’ll not put in quite as much detail here. First, we’ll check for symmetry about the x-axis. - y = 2 x3 - x5
We don’t have symmetry here since the one side is identical to the original equation and the other
isn’t. So, we don’t have symmetry about the x-axis.
Next, check for symmetry about the y-...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12