How to Algebraically Show That a Function is Even

The video tutorial explains how to determine if a function is even by substituting negative X into the function and checking for equivalence with the original function. It demonstrates that if the function remains unchanged, it is even. The tutorial also highlights that an even function's graph is symmetrical about the Y axis, which can be proven both algebraically and graphically.

What is the first step to determine if a function is even?

• Integrate the function.

• Check if the function is symmetrical about the X-axis.

• Differentiate the function.

• Substitute negative x into the function.

What does it mean if f(-x) equals f(x) for a function?

• The function is odd.

• The function is linear.

• The function is even.

• The function is undefined.

Which of the following is a characteristic of an even function's graph?

• It is symmetrical about the X-axis.

• It is symmetrical about the origin.

• It is symmetrical about the Y-axis.

• It has no symmetry.

How can you visually confirm that a function is even?

• By checking if the graph is a straight line.

• By checking if the graph is symmetrical about the origin.

• By checking if the graph is symmetrical about the X-axis.

• By checking if the graph is symmetrical about the Y-axis.

Which method can be used to prove a function is even?

• Graphical method only.

• Algebraic method only.

• Both graphical and algebraic methods.

• Neither graphical nor algebraic methods.