Question 1: A function f(x) has the property that f(-x) = f(x) for all x in its domain. What type of symmetry does this function exhibit?
Topic: Representations of Functions
- Periodic
- Linear
- Odd
- Even (Correct Answer)
Explanation
Even functions satisfy f(-x) = f(x), meaning they have symmetry about the y-axis. Classic examples include f(x) = x² and f(x) = cos(x). Odd functions would satisfy f(-x) = -f(x) instead, showing origin symmetry. Linear refers to degree, not symmetry, while periodic describes repeating patterns. Quick memory trick: even functions look the same when you fold the graph along the y-axis.