Question

math homework helpppppppppp
the graph of y= 3x^4+x^2-1 is symmetric about the.....
1. x-axis
2. y-axis
3. origin
4. none of the above

Answer 1

Well, we have even and odd symmetry. Even symmetry means we are symmetric about the y-axis and odd symmetry means we are symmetric about the origin. Here are the tests for each:
\[even: f(x) = f(-x)\]
\[odd: -f(x) = f(-x)\]
So what the first one means is we want to replace x with negative x and see if we get the same thing. So is:
\[3x ^{4}+x ^{2}-1\] the same as:
\[3(-x)^{4}+(-x)^{2}-1\]?

Answer 2

no