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To represent \( f(t) \) using a combination of Heaviside step functions based on the given graph, we need to break down the function's behavior at each point where it changes.

### Step 1: Identify Key Points and Values

1. **Initial Value**: From \( t = 0 \), the function \( f(t) \) appears to be at \( 0 \).
2. **At \( t = 1 \)**: \( f(t) \) jumps to \( 2 \), indicating a step at \( t = 1 \).
3. **At \( t = 2 \)**: \( f(t) \) increases to \( 4 \), showing a linear rise from \( 2 \) to \( 4 \).
4. **At \( t = 3 \)**: \( f(t) \) becomes constant at \( 4 \) until it drops back to \( 0 \) at \( t = 4 \).

### Step 2: Define \( f(t) \) in Terms of Heaviside Functions

Let \( h(t - c) \) represent the Heaviside function, which is \( 0 \) when \( t < c \) and \( 1 \) when \( t \ge c \).

Using this notation, we can write \( f(t) \) as follows:

1. From \( t = 0 \) to \( t = 1 \), \( f(t) = 0 \).
2. At \( t = 1 \), there is a jump to \( 2 \), which can be represented by \( 2 \cdot h(t - 1) \).
3. From \( t = 1 \) to \( t = 2 \), the function increases linearly, which can be represented by \( 2(t - 1) h(t - 1) - 2(t - 2) h(t - 2) \).
4. At \( t = 3 \), it remains at \(

Represent f(t) using a combination of Heaviside step functions. Use h(t - c) for the Heaviside function hc(t) based on the given graph.

Learn how to represent the function f(t) using Heaviside step functions based on the graph provided. This solution includes a breakdown of each section of f(t) and uses piecewise functions and Heaviside notation to model step changes at key points.

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