Question

For each equation, determine whether its graph is symmetric with respect to the x-axis, the y-axis, and the origin. Check all symmetries that apply. (a) $xy^2 + 6 = 0$ Symmetry: x-axis y-axis origin none of the above (b) $10x^2 + 24y^2 = 44$ Symmetry: x-axis y-axis origin none of the above

          For each equation, determine whether its graph is symmetric with respect to the x-axis, the y-axis, and the origin.
Check all symmetries that apply.
(a) $xy^2 + 6 = 0$
Symmetry:
x-axis
y-axis
origin
none of the above
(b) $10x^2 + 24y^2 = 44$
Symmetry:
x-axis
y-axis
origin
none of the above
        
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For each equation, determine whether its graph is symmetric with respect to the x-axis, the y-axis, and the origin.
Check all symmetries that apply.
(a) xy^2 + 6 = 0
Symmetry:
x-axis
y-axis
origin
none of the above
(b) 10x^2 + 24y^2 = 44
Symmetry:
x-axis
y-axis
origin
none of the above

Added by Alison C.

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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For each equation, determine whether its graph is symmetric with respect to the x-axis, the y-axis, and the origin. Check all symmetries that apply. (a) xy^(2)+6=0 (b) 10x^(2)+24y^(2)=44 Symmetry: Symmetry: x-axis x-axis y-axis y-axis origin origin none of the above none of the above Question7 For each equation, determine whether its graph is symmetric with respect to the x-axis, the y-axis, and the origin. Check all symmetries that apply axy+6=0 (b10x2+24y2=44 X Symmetry: Symmetry: x-axis x-axis y-axis y-axis origin none of the above origin none of the above
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Transcript

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00:05 So in this question, we're trying to see whether two equations have symmetry about the x -axis, y -axis, origin, or none of them.
00:15 It's a lot easier to see this graphically, so i graphed both functions in desmos.
00:20 The first one here in green is y -squared plus x minus 2 equals 0.
00:25 So to check whether this has axis about the, or symmetry about the y -axis, i'm going to look at where my y -axis is, which is right here.
00:35 And if i look at the left and right side of this, i do not have the same thing on the left and the right.
00:42 So it does not have symmetry about the y -axis.
00:47 If i look at the x -axis, which is this one right here, this graph is the same.
00:53 It's a reflection on the top and on the bottom.
00:56 So it does have symmetry about the x -axis.
01:00 So there is x -axis symmetry.
01:07 And in order for it to have symmetry about the origin, it has to have symmetry about the x -axis and the y -axis at the same time...
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