Determine whether the function is even, odd, or neither. Discuss the
symmetries of the graphs.

f(x)=x^4–2x^2

Any help would be appreciated. Thanks!

Step-by-step explanation:

You know the function is even because all the terms in its definition have even degree.

An even function is one that satisfies ...

  f(x) = f(-x)

An even power of -x is the same as that power of x. (-x)^2 = x^2, for example. So, a function consisting of only even-degree terms will meet the requirement for an even function. The given f(x) is an even function.

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If f(x) = f(-x), the function reflected across the y-axis is the same as the original function. That is, the y-axis is the axis of symmetry.

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1