# Which of the following equations has a graph that is symmetric with respect to the origin.

y = (x + 1)/x

y = -x^{5} + 3x

y = x^{4} - 2x^{2} + 6

y = (x - 1)^{3} + 1

y = (x^{2 }+ 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= -x^{5 }+ 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 = x^{4} - 2x^{2} + 6, by replacing x by -x,

We get y = x^{4 }- 2x^{2 }+ 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 = (x^{2 }+ 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 = x^{4} - 2x^{2} + 6 and y = (x^{2} + 1)^{2} - 1.

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