If a function is even, what can be said about its graph?

When a function is classified as even, it means that for every point ( (x, f(x)) ) on the graph of the function, the point ( (-x, f(x)) ) is also present. This characteristic leads to the conclusion that the graph is symmetrical about the y-axis.

To visualize this, consider that if you were to fold the graph along the y-axis, the two halves would align perfectly. This property is a fundamental aspect of even functions and can be observed in various examples, such as the function ( f(x) = x^2 ). For any positive or negative value of ( x ), squaring ( x ) yields the same result; hence, the values reflect symmetrically across the y-axis.

The other characteristics listed do not apply to even functions in the same way. Symmetry about the x-axis would imply that if ( (x, f(x)) ) exists, then ( (x, -f(x)) ) must also exist, which relates more to odd functions. A positive slope refers to the behavior of a line rather than symmetry, while the description of being a straight line does not encapsulate the broader category of even functions, which can take many forms,