# Symmetry

Symmetry, a fundamental concept across various disciplines, embodies balance, harmony, and proportionality. From mathematics to art, from physics to biology, symmetry plays a pivotal role in understanding the organization and structure of systems. It delineates patterns that repeat in an orderly fashion, offering insights into underlying principles governing the universe. Beyond its aesthetic appeal, symmetry serves as a powerful tool for analysis and problem-solving, enabling scientists, engineers, and artists alike to unravel complexities and create elegant solutions. In this exploration, we delve into the essence of symmetry, its significance, and its pervasive presence in our world.

- How do you determine whether the graph of #g(x)=(x^2-1)/x# is symmetric with respect to the origin?
- How do you determine whether the graph of #f(x)=1/x-x^100# is symmetric with respect to the origin?
- Is the function #f(x) = x^2# symmetric with respect to the y-axis?
- Is the function #f(x) = 5x^6 + 8x^2 – 16# even, odd or neither?
- How do you determine whether the graph of #f(x)=1/(5x)-x^19# is symmetric with respect to the origin?
- How do you determine whether the graph of #y=-8x# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?
- Is the function #2 sin x cos x# even, odd or neither?
- Is the function #f(x) = x^5 - 16x# even, odd or neither?
- How do you determine whether the graph of #absy=x^3# is symmetric with respect to the x, y axis?
- Is the function #h(x) = x^3-5# even, odd or neither?
- Is the function #f(x) = x^3 + x sin^2 x# even, odd or neither?
- Is the function #f(x)=(1/x^3+x)^5# even, odd or neither?
- Is the function #f(x) = x^3# symmetric with respect to the y-axis?
- Is the function #f(x)=x^-6# even, odd or neither?
- Is the function #f(x) = cos x# even, odd or neither?
- Is the function #f(x)= -4x^2 + 4x# even, odd or neither?
- What is the line of symmetry for #f(x) = x^4#?
- How do you determine whether the graph of #absy=xy# is symmetric with respect to the x axis, y axis or neither?
- Is the function #f(x) = 2 cot x# even, odd or neither?
- Consider the function #f(x)= 9x-x^3#. Is this function odd, even, or neither?