Understanding Unit Step Functions

The video tutorial explains how to write an equation for a graph using the unit step function, also known as the Heaviside step function. It defines the unit step function and demonstrates how to represent a given piecewise function using this method. The tutorial walks through the process of analyzing the graph, identifying intervals, and applying the unit step function to express the function values over specific intervals. The lesson concludes with the final expression of the function using unit step functions.

What is another name for the unit step function?

• Sigmoid function

• Gaussian function

• Dirac delta function

• Heaviside step function

In a piecewise function, what is the value of the function outside the interval from 1 to 4?

• 3

• 0

• 1

• Undefined

How is the function value expressed using unit step functions over the interval from 1 to 4?

• 3 * U sub 1 of T + 3 * U sub 4 of T

• U sub 1 of T - 3 * U sub 4 of T

• 3 * U sub 1 of T + U sub 4 of T

• 3 * U sub 1 of T - U sub 4 of T

What happens to the function value when T is less than 1?

• It becomes undefined

• It remains 0

• It becomes 1

• It becomes 3

What is the function value when T is greater than or equal to 4?

• 3

• 1

• 0

• Undefined

What is the result of multiplying the function value by the difference of two unit step functions over the interval from 1 to 4?

• Undefined

• 3

• 1

• 0

What is the value of F(T) in the final expression?

• 1

• 3

• 4

• 0

What is the value of 'a' in the final expression?

• 1

• 3

• 4

• 0

What is the value of G(T) in the final expression?

• 0

• 1

• 4

• 3

What is the value of 'b' in the final expression?

• 0

• 3

• 4

• 1