Which of the following equations has a graph that is symmetric with respect to the origin.
y = (x + 1)/x
y = -x5 + 3x
y = x4 - 2x2 + 6
y = (x - 1)3 + 1
y = (x2 + 1)2 - 1
Solution:
Given a set of equations
In order to check the symmetry of reflection, we need to replace x by -x and still should get the same function after transformation.
1. Consider y= (x + 1)/x
Replace x by -x in the first equation,
We get y= (-x + 1)/-x, which is not the given equation.
Hence, the first equation doesn't follow the symmetry property of reflection.
2. Consider second equation y= -x5 + 3x, by replacing x by -x,
We get y= -(-x)5 + 3x
Hence, the second equation also doesn't follow the symmetry property of reflection.
3. Consider third equation y = x4 - 2x2 + 6, by replacing x by -x,
We get y = x4 - 2x2 + 6, which is the same given equation
Hence, the third equation follows the symmetric property of reflection.
4. Consider fourth equation y = (x - 1)3 + 1, by replacing x by -x,
We get y= (-x - 1)3 + 1, which is not the same as given.
Hence, the fourth equation doesn't follow the symmetry property of reflection.
5. Consider fifth equation y = (x2 + 1)2 - 1, by replacing x by -x,
We get that same function
Hence, the fifth equation follows the symmetry property of reflection.
Which of the following equations has a graph that is symmetric with respect to the origin.
Summary:
The following equation has a graph that is symmetric with respect to the origin y = x4 - 2x2 + 6 and y = (x2 + 1)2 - 1.
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