Identifying Even and Odd Functions

The video tutorial explains how to determine if a function is odd or even by examining the exponents and testing the function's symmetry. It involves substituting negative x into the function and simplifying to see if the function remains unchanged or becomes its negative. The example provided shows that the function is even as it remains unchanged after simplification.

What might you initially think when you see all exponents are odd?

• The function is odd.

• The function is undefined.

• The function is linear.

• The function is even.

What must be checked to confirm if a function is even?

• If f(x) equals -f(x)

• If f(x) equals f(-x)

• If f(x) equals x

• If f(x) equals 0

What must be checked to confirm if a function is odd?

• If f(x) equals x

• If f(x) equals f(-x)

• If f(x) equals -f(x)

• If f(x) equals 0

What is the first step in testing the nature of a function?

• Divide the function by X

• Multiply the function by 2

• Substitute negative X into the function

• Add a constant to the function

What happens when you substitute negative X into the function?

• The function becomes zero

• The function changes sign

• The function remains the same

• The function becomes undefined

What is the result of factoring out the negative from the denominator?

• The function becomes zero

• The function doubles

• The negatives cancel out

• The function becomes undefined

What conclusion is reached after simplification?

• The function is undefined

• The function is even

• The function is linear

• The function is odd

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

• The function is undefined

• The function is even

• The function is odd

• The function is linear

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

• The function is linear

• The function is undefined

• The function is even

• The function is odd

What is the significance of the function's symmetry?

• It shows the function is undefined

• It determines if the function is linear

• It indicates the function is quadratic

• It helps identify if the function is even or odd