Question

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

Which statement is true?
Neither function is an even function.


Only the function g(x) is an even function.


Both functions are even functions.


Only the function f(x) is an even function.


Thank you!

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.