Symmetry of a Function

Question

What is f(x)=(2/5)x+1 symmetric to? Is it the y-axis, the x-axis, or the origin?

Answer 1

It has none of those symmetries. If you actually graph the line, it shouldd be obvious that none of those work. A line does, however, always have point and line symmetry. Any line perpendicular to your line will work as an axis of symmetry and any point on the line will act as a point of symmetry. So for example, y=(-5/2)x+12 is a line of symmetry and the point (20,9) is a point of symmetry. There are an infinite number of symmetries for your example.