Exploring Even and Odd Functions

What is the general form of the function discussed in today's notes?

• f(x) = ax^2 + bx + c

• f(x) = ax + b

• f(x) = a(x - h)^2 + k

• f(x) = a(x - h) + k

In Example 1, what happens to the function f(x) = 2x when x is replaced with -x?

• It becomes 2x

• It becomes -2x

• It remains unchanged

• It becomes 2x^2

What type of function is f(x) = 2x if it changes to -2x when x is replaced with -x?

• Even

• Odd

• Both

• Neither

In Example 2, what is the result of replacing x with -x in the function g(x) = -x^2 - 2?

• It remains unchanged

• It becomes -x^2 + 2

• It becomes x^2 - 2

• It becomes -x^2 - 2

What type of function is g(x) = -x^2 - 2 if it remains unchanged when x is replaced with -x?

• Even

• Odd

• Both

• Neither

In Example 3, what is the result of replacing x with -x in the function h(x) = 2x^2 - x - 2?

• It becomes 2x^2 - x - 2

• It becomes 2x^2 + x - 2

• It becomes -2x^2 + x + 2

• It remains unchanged

What type of function is h(x) = 2x^2 - x - 2 if it changes partially when x is replaced with -x?

• Even

• Odd

• Neither

• Both

What is the simplified form of f(x) = 5(-x) in the practice problems?

• -5x^2

• -5x

• 5x^2

• 5x

What type of function is f(x) = 5(-x) if it simplifies to -5x?

• Even

• Odd

• Neither

• Both

What type of function is g(x) = 2^(-x) if it cannot be simplified further?

• Even

• Both

• Odd

• Neither