Understanding Unit Step Functions

This video tutorial explains how to write the equation of a graph using the unit step function, also known as the Heaviside step function. It covers the definition of the unit step function, the process of defining a piece-wise function, finding the equation of a line, and applying unit step functions to define intervals. The tutorial also includes steps to simplify the function and presents the final form of the function.

What is the value of the unit step function U(t - C) when t is less than C?

• 0

• C

• 1

• t

In a piece-wise function, what is the slope of the line segment between points (4,0) and (8,3)?

• 2

• 1

• 4/3

• 3/4

How is the unit step function used to express a piece-wise function?

• By subtracting constant values

• By multiplying with differences of unit step functions

• By dividing by unit step functions

• By adding constant values

What happens to the function value when T is greater than or equal to 8?

• It becomes zero

• It becomes three

• It becomes one

• It remains unchanged

What is the purpose of factoring out U sub 8 of T in the simplification process?

• To simplify the expression

• To change the function's domain

• To increase the function value

• To eliminate the unit step function

What is the result of distributing 3/4s in the expression?

• It changes the slope

• It alters the domain

• It simplifies the function

• It factors out constants

Why is it important to have the function in the second form for transformations?

• It is the only acceptable form

• It looks more complex

• It is required for the Laplace transform

• It is easier to calculate

What does the expression 34 * (t - 4) * U sub4 of t represent?

• A quadratic function

• A linear segment of the piece-wise function

• An exponential function

• A constant function

What is the significance of having T minus 4 and T minus 8 in the final form?

• They simplify the calculation

• They are arbitrary constants

• They are used for decoration

• They define the intervals of the piece-wise function

What is the value of G of T in the final form?

• -34s * (T - 8)

• 34s * (T - 4)

• 34s * (T - 8)

• -34s * (T - 4)