Symmetry

Key Questions

• What is a line of symmetry?

  Answer:

  It is a line about which the shape/curve is repeated as if it had rotated about it by #180^o#
  See diagram/graph

  Explanation:

  

  #color(green)("The line of symmetry is the y axis")#

  Tony B · 1 · Nov 5 2015
• What are some examples of a symmetric function?

  Answer:

  #f(x, y) = x^2 + xy + y^2#
  #g(x, y, z) = xy + yz + zx + 1/(x^2+y^2+z^2)#

  Explanation:

  A symmetric function is a function in several variable which remains unchanged for any permutation of the variables.

  For example, if #f(x, y) = x^2 + xy + y^2#, then #f(y, x) = f(x, y)# for all #x# and #y#.

  George C. · 3 · Jul 15 2015
• What is rotational symmetry?

  Answer:

  How many times is the same shape seen if a figure is turned through 360°

  Explanation:

  Symmetry means that there is a 'sameness' about two figures THere are two types of symmetry - line symmetry and rotational symmetry.

  Line symmetry means if you draw a line thorugh the middle of a figure, the one side is a mirror image of the other.

  Rotational symmetry is the symmetry of turning.

  If you turn a shape though 360°, sometimes the identical shape is seen again during the turn. This is called rotational symmetry.

  For example, a square has 4 sides, but the square will look exactly the same no matter which of its sides is at the top.

  Rotational symmetry is described by the number of times the same shape is seen during the 360° rotation.

  A square has rotational symmetry of order 4,
  An equilateral triangle has rotational symmetry of order 3.
  A rectangle and a rhombus have rotational symmetry of order 2.

  A regular pentagon has rotational symmetry of order 5.

  EZ as pi · 2 · Sep 7 2016

• What functions have symmetric graphs?
• What are some examples of a symmetric function?
• What is a line of symmetry?
• What is rotational symmetry?
• Is the function #f(x) = x^2# symmetric with respect to the y-axis?
• Is the function #f(x) = x^2# symmetric with respect to the x-axis?
• Is the function #f(x) = x^3# symmetric with respect to the y-axis?
• What is the line of symmetry for #f(x) = x^4#?
• Is the graph of the function #f(x) = 2^x# symmetric?
• Is #f(x)=x^2+sin x# an even or odd function?
• Is the product of an odd function and an even function odd or even?
• Is the function #f(x) = x^3 + x sin^2 x# even, odd or neither?
• Is the function #f(s) = 4s^(3/2) # even, odd or neither?
• Is the function #f(X) = 4X^2 + X^4 -120# even, odd or neither?
• Is the function #f(x)=x^-6# even, odd or neither?
• Is the function #f(x)=x^4+3x^-4+2x^-1# even, odd or neither?
• Is the function #f(x)=x^4-6^-4+3x^2# even, odd or neither?
• Is the function #f(x)=-5x^4-3x^-4-2# even, odd or neither?
• Is the function #f(x) = x^5 - 16x# even, odd or neither?
• Is the function #(2-x)^(1/3)# even, odd or neither?
• Is the function #f(x)=1/(x^3+1)# even, odd or neither?
• Is the function #f(x)=2x^4+3x^2# even, odd or neither?
• Is the function #f(x)=(1/x^3+x)^5# even, odd or neither?
• Is the function #f(x) = 13x^4 – 2x^3 + 7x# even, odd or neither?
• Is the function #f(x) = 5x^6 + 8x^2 – 16# even, odd or neither?
• Is the function #f(x) =x sin x# even, odd or neither?
• Is the function #f(x) =cosx sinx# even, odd or neither?
• Is the function #f(x) = x^6-2x^2+3# even, odd or neither?
• Is the function #h(x) = x^3-5# even, odd or neither?
• Is the function #g(x) = x^3-5x# even, odd or neither?
• Is the function #f(x)=x^2/(x-1)# even, odd or neither?
• Is the function #f(x) = cos x# even, odd or neither?
• Is the function #f(x) = sin x# even, odd or neither?
• Is the function #f(x) = 2 cot x# even, odd or neither?
• Is the function #f(x) = (x^2+8)^2# even, odd or neither?
• Is the function #f(x)= 6x^3 - 2x# even, odd or neither?
• Is the function #f(x)= -4x^2 + 4x# even, odd or neither?
• Is the function #2 sin x cos x# even, odd or neither?
• How do you test for symmetry with respect to the line y=-x?
• 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 #6x^2=y-1# is symmetric with respect to the x, y axis, the line y=x, the line y=-x, or none of these?
• How do you determine whether the graph of #x^3+y^3=4# is symmetric with respect to the x, y axis, the line y=x, the line y=-x, or none of these?
• How do you determine whether the graph of #y=sqrt(2-x^2)# is symmetric with respect to the x, y axis?
• How do you determine whether the graph of #absy=x^3# is symmetric with respect to the x, y axis?
• How do you determine whether the graph of #f(x)=5x^2+6x+9# is symmetric with respect to the origin?
• How do you determine whether the graph of #f(x)=1/(4x^7)# 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?
• 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 #x+y^2=1# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?
• 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?
• How do you determine whether the graph of #y=1/x^2# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?
• How do you determine whether the graph of #y^2=(4x^2)/9-4# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?
• How do you determine whether the graph of #y^2=x^2# is symmetric with respect to the x axis, y axis or neither?
• How do you determine whether the graph of #absx=-3y# is symmetric with respect to the x axis, y axis or neither?
• How do you determine whether the graph of #y^2+3x=0# is symmetric with respect to the x axis, y axis or neither?
• How do you determine whether the graph of #absy=2x^2# is symmetric with respect to the x axis, y axis or neither?
• How do you determine whether the graph of #absy=xy# is symmetric with respect to the x axis, y axis or neither?
• Question #93699
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• Question #2c359