To determine which statements are true for the functions g(x) = x² and h(x) = x², we need to first recognize that both functions are identical. They represent the same mathematical relationship where the output is the square of the input.
- Both functions are even functions: True. An even function is defined as a function where f(-x) = f(x) for all x in the domain. Since g(x) and h(x) yield the same results for both positive and negative values of x, they are even.
- Both functions have a minimum value at x = 0: True. The vertex of the parabola described by both functions is at (0, 0), which is the lowest point on the graph.
- Both functions are increasing for x > 0: True. For x greater than 0, as x increases, g(x) and h(x) also increase because the derivative of x² is positive.
- Both functions are decreasing for x < 0: True. For x less than 0, as x increases towards 0, g(x) and h(x) are decreasing because again, the derivative is negative.
In summary, since g(x) and h(x) are the same function, all statements regarding their properties that apply to one will apply to the other.