Algebraically Determine If a Function is Even or Odd

The video tutorial explains how plugging in negative X into a function and raising it to an even power results in a positive number. This is because any negative number raised to an even power is positive. The tutorial further compares this result to the original function, demonstrating that it is an example of an even function.

What is the first step in analyzing a function with negative inputs?

• Substitute negative values into the function

• Multiply by a positive constant

• Divide by a negative constant

• Add a constant to the function

What happens when a negative number is raised to an even power?

• It becomes zero

• It becomes positive

• It remains unchanged

• It becomes negative

Why is a negative number raised to an even power always positive?

• Because the function is odd

• Because negative numbers are inherently positive

• Because even powers cancel out the negative sign

• Because the function is linear

How does the function relate to the concept of even functions?

• It is an example of a quadratic function

• It is an example of an odd function

• It is an example of a linear function

• It is an example of an even function

What characteristic of the function confirms it as an even function?

• The function is symmetric about the origin

• The function has no symmetry

• The function is symmetric about the x-axis

• The function is symmetric about the y-axis