Question

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

Answer 1

A. Absolute value.

Explanation:

We are asked to determine the type of function, if it is symmetric over the line
`x=2`.

We know that a line of form
`x=a` represents an equation of a vertical line that crosses x-axis at point
`(2,0)` parallel to y-axis.

We know that a cubic function is symmetric about origin, while an exponential function has no symmetry.

A rational function is not necessarily symmetric to y-axis.

We know that an absolute value function is symmetric about y-axis, so our given function will be symmetric to the line
`x=2` and option A is the correct choice.