How to understand even functions and how we can determine a function is even

The teacher engages students in a discussion about even functions, focusing on their symmetry properties. Students are asked to recall what they know about even functions, particularly their symmetry about the Y-axis. The teacher explains the concept of symmetry using examples and defines even functions as those where f(-x) equals f(x). The session concludes with a warm-up exercise to reinforce the concept.

What type of symmetry is characteristic of even functions?

• Symmetry about the origin

• No symmetry

• Symmetry about the Y-axis

• Symmetry about the X-axis

In the context of even functions, if f(x) = 3, what is f(-x)?

• f(-x) = 3

• f(-x) = -3

• f(-x) = x

• f(-x) = 0

Which of the following is true for an even function?

• f(x) = 0

• f(x) = -f(-x)

• f(x) = f(-x)

• f(x) = x

If a function is even, what happens when you substitute -x into the function?

• You get the original function

• The function value doubles

• The function becomes undefined

• You get a different function

What should you understand about even functions if no graph is provided?

• They are always increasing

• They are always decreasing

• f(-x) equals f(x)

• They have symmetry about the X-axis