The functions that have an axis of symmetry at x = 2 will reflect symmetrically across the line x = 2. To determine which functions meet this criterion, we can consider several types:
- Quadratic functions: A general quadratic function is in the form of f(x) = a(x-h)^2 + k, where (h, k) is the vertex. For the function to be symmetric about x = 2, h must equal 2.
- Linear functions: These do not have a point of symmetry, but if defined properly (like in piecewise functions), they can reflect across a vertical line.
- Absolute value functions: A function in the form of f(x) = |x – 2| will also have a symmetry around x = 2 since the absolute value reflects all values to the left of x = 2 back to the right, maintaining symmetry.
To summarize, check functions that have their vertex or a point of symmetry at x = 2. Particularly, look for quadratics and certain absolute value functions to confirm.