Understanding the Signum Function

The video tutorial introduces the Signum function, explaining its values, graph, and relation to the absolute value function. It describes how the Signum function can be expressed as a piecewise function with values of -1, 0, and 1, and sketches its graph. The tutorial also covers the Signum function's role as the derivative of the absolute value function, except at zero, and demonstrates how any real number can be expressed as the product of its absolute value and its Signum function.

What are the possible values of the Signum function?

• 0, 1

• -1, 1

• -2, 0, 2

• -1, 0, 1

What is the y-value of the Signum function when X is greater than zero?

• -1

• 0

• Undefined

• 1

How does the Signum function relate to the absolute value of x divided by x?

• They are never equal

• They are equal except at x=0

• They are equal for negative x only

• They are equal only at x=0

What happens to the Signum function at x=0?

• It is undefined

• It equals 0

• It equals -1

• It equals 1

What is the derivative of the absolute value function when x is not zero?

• Quadratic function

• Signum function

• Constant function

• Linear function

What is the slope of the absolute value function on the right side of the graph?

• 1

• 0

• Undefined

• -1

How can any real number be expressed using the Signum function?

• As the difference of its absolute value and Signum function

• As the product of its absolute value and Signum function

• As the quotient of its absolute value and Signum function

• As the sum of its absolute value and Signum function

What is the Signum function of a negative number?

• 0

• 1

• -1

• Undefined

What is the result of multiplying the absolute value of zero by the Signum function of zero?

• -1

• Undefined

• 0

• 1

Does the method of expressing numbers using the Signum function work for imaginary numbers?

• Only for negative imaginary numbers

• Only for positive imaginary numbers

• No, never

• Yes, always