Question

write the step function shown in the graph.
graph with x - axis (marked 2, 4) and y - axis (marked 2, 4), showing step - like blue dots and open circles
$f(x)=\

$$\begin{cases}\\square, & \\text{if } 2\\leq x<3 \\\\ \\square, & \\text{if } 3\\leq x<4 \\\\ \\square, & \\text{if } 4\\leq x<5 \\end{cases}$$

$

Explanation:

Step1: Analyze the graph for \(2 \leq x < 3\)

Looking at the graph, when \(2 \leq x < 3\), the \(y\)-value (the value of the step function) is 1. So the first box should be 1.

Step2: Analyze the graph for \(3 \leq x < 4\)

For the interval \(3 \leq x < 4\), the \(y\)-value of the step function is 2. So the second box should be 2.

Step3: Analyze the graph for \(4 \leq x < 5\)

In the interval \(4 \leq x < 5\), the \(y\)-value of the step function is 3. So the third box should be 3.

Answer:

\(f(x)=

$$\begin{cases}1, & \text{if } 2\leq x < 3 \\2, & \text{if } 3\leq x < 4 \\3, & \text{if } 4\leq x < 5\end{cases}$$

\)