Question

For each equation, determine whether its graph is symmetric with respect to the -axis, the -axis, and the origin.

4y^4+24x^2=28 and y=1/x^2+5

Check all symmetries that apply

x-axis,y-axis,origin or non of the above.

Answer 1

You need parentheses for the 2nd equation.

Is this,
y = 1/(x^2 + 5)

Or,
y = 1/(x^2) + 5

Answer 2

Sorry y=1/(x^2+5)

Answer 3

4y^4 + 24x^2 = 28

Symmetric to x-axis if an equivalent equation is obtained when y is replaced by -y.

4y^4 + 24x^2 = 28
4(-y)^4 + 24x^2 = 28
4y^4 + 24x^2 = 28

Since, the two equations are equivalent, the graph is symmetric to the x-axis.

Symmetric to y-axis if an equivalent equation is obtained when x is replaced by -x.

4y^4 + 24x^2 = 28
4y^4 + 24(-x)^2 = 28
4y^4 + 24x^2 = 28

Since, the two equations are equivalent, the graph is symmetric
to the y-axis.

Symmetric to the origin if an equivalent equation is obtained when x is replaced by -x and y is replaced by -y.

4y^4 + 24x^2 = 28
4(-y)^4 + 24(-x)^2 = 28
4y^4 + 24x^2 = 28

Since, the two equations are equivalent, the graph is symmetric
to the origin.

I'll leave the 2nd equation for you to try.

Answer 4

I get that the second equation x-axis. Is that right?

Answer 5

Symmetric to y-axis if an equivalent equation is obtained when x is replaced by -x.

It is symmetric to the y-axis, not x-axis.