How does the Heaviside unit step function affect the graph of a function when it is applied, specifically for f(t) = u(t - c) - sin(t - c)?

The Heaviside unit step function, u(t - c), causes the function f(t) = u(t - c) - sin(t - c) to be zero for all t less than c and to equal -sin(t - c) for t greater than or equal to c. This results in the graph being suppressed before t = c and displaying the behavior of -sin(t - c) starting at t = c.

The Heaviside unit step function effectively 'turns on' the function -sin(t - c) at t = c, while maintaining a value of zero for all t < c. Therefore, the graph of f(t) = u(t - c) - sin(t - c) will show no values until t reaches c, at which point it will follow the curve of -sin(t - c). This creates a discontinuity in the graph at t = c, where it transitions from 0 to the negative sine function.