Larn How to Determine Algebraically If a Function is Odd or Not

The video tutorial explains how to determine if a function is even or odd by evaluating F(-X). If F(-X) equals the original function, it is even. If F(-X) results in the opposite of the original function, it is odd. The tutorial also covers checking graph symmetry about the X and Y axes to confirm the function's nature.

What is the condition for a function to be classified as even?

• F of negative X equals the opposite of the original function

• F of negative X equals zero

• F of negative X is undefined

• F of negative X equals the original function

How can you determine if a function is odd?

• F of negative X equals the opposite of the original function

• F of negative X equals zero

• F of negative X is undefined

• F of negative X equals the original function

What is the result of applying the distributive property to the opposite of F of X?

• 2X cubed plus 3X + X

• -2X cubed minus 3X - X

• 2X cubed minus 3X - X

• -2X cubed plus 3X + X

Which of the following describes the symmetry of an odd function's graph?

• Not symmetrical at all

• Symmetrical about both the X and Y axes

• Symmetrical about the Y axis only

• Symmetrical about the X axis only

If a function is symmetrical about both the X and Y axes, what type of function is it likely to be?

• Even

• Odd

• Neither even nor odd

• Undefined