Question

The graph of g(x) is a parabola with a vertex at (0, 2).

Answer 1

The function g(x) has vertex (0,2) and the function of the graph has vertes (-2,0), so this latter is the function f(x).

Now analyze the statements.

Neither function is an even function ---> FALSE because the fact that the function g(x) has vertex (0,2) means that the symmetry axis of the parabole is the y-axis, so you know that g(x) = g(-x) which is the definition of an even function.

Only the function g(x) is an even function ---> TRUE: I already explained you why you can tell that g(x) is even. Now you just mut observe the graph of f(x) to realize that f(x) is not equal to f(-x) which means that it is not even.

Both functions are even functions ---> FALSE as we stated above f(x0 is not even.

Only the function f(x) is an even function ---> FALSE as we stated above.