Determine algebraically whether the graph is symmetric with respect to the \( x \)-axis, the \( y \)-axis, and the origin.
\[
x^{2}+2 y^{4}=5
\]
A. \( y \)-axis only
B. \( x \)-axis only
C. Origin only
D. \( x \)-axis, \( y \)-axis, origin

Answer

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Answer

Answer: D. \( x \)-axis, \( y \)-axis, origin

Steps

Step 1 ：Replace y with -y in equation x^2 + 2y^4 = 5: (x^2 + 2(-y)^4 \text{ unchanged })

Step 2 ：Replace x with -x in equation x^2 + 2y^4 = 5: ((-x)^2 + 2y^4 = 5 \text{ unchanged })

Step 3 ：Replace both x with -x and y with -y in equation x^2 + 2y^4 = 5: ((-x)^2 + 2(-y)^4 = 5 \text{ unchanged })

Step 4 ：Answer: D. \( x \)-axis, \( y \)-axis, origin