Final answer:
Even functions are not necessarily symmetrical about the y-axis. Evenness refers to the condition y(x) = y(-x), while symmetry about the y-axis is a specific type of evenness. Some even functions, are not symmetrical about the y-axis.
Step-by-step explanation:
An even function is a function that satisfies the condition y(x) = y(-x). It means that if you replace the variable x with its negation (-x) in the function, the result will be the same. The symmetry of an even function is about the y-axis, which means that if you fold the graph of the function along the y-axis, the two halves will match.
However, it is important to note that not all functions that satisfy the condition y(x) = y(-x) are symmetric about the y-axis. There can be functions that are even but not symmetrical about the y-axis. Symmetry about the y-axis is just one specific type of evenness.
For example, the function is even, but it is not symmetric about the y-axis. If you plot the graph of this function, you will see that it is a parabola that opens upwards, but it is not symmetric with respect to the y-axis.