draw the graph of function. `y=(|x|-x)/(2)`

Answer

To draw the graph of the function \( y = \frac{|x| - x}{2} \), we will analyze the function based on the definition of the absolute value and then plot the graph accordingly.

### Step-by-Step Solution:

1. **Understand the function**: The function involves the absolute value of \( x \). The absolute value function \( |x| \) behaves differently based on whether \( x \) is non-negative or negative.

2. **Case 1: When \( x \geq 0 \)**:
- Here, \( |x| = x \).
- Substitute into the function:
\[ y = \frac{|x| - x}{2} = \frac{x - x}{2} = \frac{0}{2} = 0 \]
- Therefore, for \( x \geq 0 \), \( y = 0 \).

3. **Case 2: When \( x < 0 \)**:
- Here, \( |x| = -x \).
- Substitute into the function:
\[ y = \frac{|x| - x}{2} = \frac{-x - x}{2} = \frac{-2x}{2} = -x \]
- Therefore, for \( x < 0 \), \( y = -x \).

4. **Summarize the function**:
- For \( x \geq 0 \): \( y = 0 \)
- For \( x < 0 \): \( y = -x \)

5. **Plot the graph**:
- For \( x \geq 0 \), the graph is a horizontal line along the x-axis at \( y = 0 \).
- For \( x < 0 \), the graph is a straight line with a slope of -1 (which means it goes downwards) starting from the origin (0,0) and extending into the negative x-axis.

6. **Draw the axes**:
- Draw the x-axis and y-axis on a graph paper.
- Mark the points for \( y = 0 \) from \( x = 0 \) to positive infinity.
- Draw the line \( y = -x \) from the origin (0,0) to the left (negative x-axis).

### Final Graph:
- The graph consists of a horizontal line along the x-axis for \( x \geq 0 \) and a line with a slope of -1 for \( x < 0 \).