Please give me an example of?

Question

1)function which is symmetric about the y axis

2)symmetric about the origin (which can also be seen as a reflection in the x AND y axes) i mean odd

3)symmetry about the vertical line through the vertex, but not in the x axis, y axis or origin, and so is neither even nor odd

Answer 1

1)

f(x) = 3x^4 + 6x² -6

f(x) = 6x^6 - x^4 + 12x² +5

f(x) = 9x^8 -x^4 + 5

every funktion with just even potens *

2)

f(x) = 2x³ + 4x

f(x)  = 4x^5 -3x³ -12x

f(x) = 7x^13 - 5x^7 + x

every funktion with just odd potenz *

3)

f(x) = 2x² -4x+ 6

f(x) = x² -5x +1

f(x) = -3x² +12x

every funktion in form ax² + bx+c

a and b must be numbers except zero

there are more funktions , I just picked some examples

*) all funktions are polynom funktions.

Answer 2

1) y = x^2

2) y = x^3

3) y = (x-1)^2

Answer 3

1) f(x)=x^2

2) f(x)=1/x

3) f(x)=sinh(x)