Question

if a function is symmetry over the line x=2, what kind of function could it be ? A . absolute value B. cubic C . exponential D . rational

Answer 1

Answer:  The answer is (A) Absolute value.

Step-by-step explanation:  Given that we have a function which is symmetric over the line x = 2.

Obviously, the graph of the line x = 2 will be vertical, parallel to Y-axis.

But, the graphs of a cubic function, exponential function and a rational function will not be always parallel to the Y-axis. So, these three options will not work here.

The only correct choice is the absolute function.

For example, for the given line x = 2, the function which is symmetric to it will be of the form

$|x-2|=k,$

where 'k' is any real number.

The attached figure is drawn for k=2.

Thus, the correct option is (A). Absolute value.