Question

Which option correctly represents the graph of f(x) = 1/3x^2+2 and describes

whether the function is even or odd?
(I just need to know if it’s even or odd)

Answer 1

the function is even

Answer 2

The f(x) is an even function.

The graph of f(x) = 1/3x^2 + 2 is a parabola that opens upwards, with its vertex at the point (0, 2). This is because the coefficient of the x^2 term is positive, indicating that the parabola is concave up. Additionally, the constant term is positive, shifting the entire parabola upwards by 2 units.

The function f(x) = 1/3x^2 + 2 is an even function. This means that for every input value x, the output value f(-x) is equal to f(x). In other words, the graph of f(x) is symmetrical about the y-axis.

Here's a more detailed explanation of why f(x) is an even function:

f(-x) = 1/3(-x)^2 + 2 = 1/3x^2 + 2 = f(x)

Since f(-x) is equal to f(x) for every input value x, f(x) is an even function.