Expert: Steve Holleran - 10/23/2007

Question
decide whether the equations have symmetry around the x-axis, the y-axis, the origin, or none of them.
1) f(x)= 4x^2-2x+3
2) f(x)= 2x^5-3x+1
3) f(x)= -x^3+2x

Answer
Hi Dave,

To do this, in each case you want to find f(-x) and compare it to f(x).

If f(-x) = f(x), then f has y-axis symmetry.

If f(-x) = -f(x), the f has origin symmetry

None of them will have x-axis symmetry, because if they did, they would not pass the vertical line test, and would not be functions.

1) f(-x) = 4(-x)^2 - 2(-x) + 3

        = 4x^2 + 2x + 3        no symmetry

2) f(-x) = 2(-x)^5 - 3(-x) + 1

        = -2x^5 + 3x + 1       no symmetry

3) f(-x) = -(-x)^3 + 2(-x)

        = -(-x^3) - 2x

        = x^3 - 2x    = -f(x) so origin symmetry

Hope this is what you needed
Steve