Heaviside Function Concepts

The video introduces the Heaviside or unit step function, explaining its definition and uses, such as modeling circuits. It covers graphing Heaviside functions, analyzing differences between them, and generalizing their application. The video also demonstrates graphing a quadratic function using Heaviside functions and previews the next video on piecewise functions.

What is another name for the Heaviside function?

• Unit step function

• Sine function

• Exponential function

• Logarithmic function

What is the value of the Heaviside function when T is less than zero?

• Undefined

• T

• 0

• 1

How does the graph of h(t-1) differ from the original Heaviside function?

• Shifted down by 1 unit

• Shifted left by 1 unit

• Shifted right by 1 unit

• Shifted up by 1 unit

At what value of T does the function h(t-1) - h(t+3) turn on?

• T = 2

• T = 1

• T = 3

• T = 0

What happens to the function h(t-1) - h(t+3) at T = 3?

• It turns on

• It turns off

• It remains constant

• It becomes undefined

What is the effect of multiplying the Heaviside function by another function G(t)?

• It scales the graph

• It changes the value to G(t)

• It changes the interval

• It shifts the graph

What does the graph of f(t) = t^2 look like between T = 1 and T = 2?

• A constant function

• A sine wave

• A parabola

• A straight line

What will be covered in the next video?

• Exploring exponential functions

• Using Heaviside functions for a piecewise function

• Graphing a sine function

• Understanding logarithmic functions