Explanation:
An even function is a function that satisfies the property f(x) = f(-x) for all values of x in the domain. In other words, if you replace x with -x in the function, the result will be the same.

When we graph an even function, the graph will be symmetrical about the y-axis. This means that if we reflect one side of the graph over the y-axis, we will get the other side of the graph.

Graphing an even function:
To understand why the graph of an even function is symmetrical about the y-axis, let's consider the graph of a simple even function, f(x) = x^2.

If we substitute -x for x in this function, we get f(-x) = (-x)^2 = x^2. This shows that the function is even.

If we plot some points on this graph, we can see the symmetry about the y-axis:

x = -2, f(x) = (-2)^2 = 4
x = -1, f(x) = (-1)^2 = 1
x = 0, f(x) = 0^2 = 0
x = 1, f(x) = 1^2 = 1
x = 2, f(x) = 2^2 = 4

If we plot these points on a graph, we can see that the graph is symmetrical about the y-axis. The points on one side of the graph mirror the points on the other side.

Generalizing for any even function:
This same symmetry applies to any even function. If we substitute -x for x in an even function, we will get the same function back.

For example, if we have an even function f(x) = x^4 + 2x^2, substituting -x for x gives f(-x) = (-x)^4 + 2(-x)^2 = x^4 + 2x^2. This shows that the function is even.

The graph of this function will also be symmetrical about the y-axis. If we reflect one side of the graph over the y-axis, we will get the other side of the graph.

Therefore, the correct answer is option B, the graph y = f(x) will be symmetrical about the y-axis if f(x) is an even function.