Graph each function. `y=|x|+x,-2lexle2`

Answer

To graph the function \( y = |x| + x \) for \( -2 \leq x \leq 2 \), we will analyze the function based on the definition of the absolute value function.

### Step 1: Understand the function
The function \( y = |x| + x \) can be broken down into two cases based on the value of \( x \):
- For \( x \geq 0 \): \( |x| = x \), so \( y = x + x = 2x \).
- For \( x < 0 \): \( |x| = -x \), so \( y = -x + x = 0 \).

### Step 2: Determine the intervals
We need to evaluate the function on the intervals defined by the question:
- From \( -2 \) to \( 0 \): Here, \( y = 0 \).
- From \( 0 \) to \( 2 \): Here, \( y = 2x \).

### Step 3: Calculate points for the graph
- For \( -2 \leq x < 0 \):
- At \( x = -2 \): \( y = 0 \)
- At \( x = -1 \): \( y = 0 \)
- At \( x = 0 \): \( y = 0 \)

- For \( 0 \leq x \leq 2 \):
- At \( x = 0 \): \( y = 0 \)
- At \( x = 1 \): \( y = 2(1) = 2 \)
- At \( x = 2 \): \( y = 2(2) = 4 \)

### Step 4: Plot the points
Now we can plot the points on the graph:
- For the interval \( -2 \leq x < 0 \), the graph is a horizontal line along the x-axis from \( (-2, 0) \) to \( (0, 0) \).
- For the interval \( 0 \leq x \leq 2 \), the graph is a straight line starting from \( (0, 0) \) to \( (1, 2) \) and then to \( (2, 4) \).

### Step 5: Draw the graph
- Draw a horizontal line from \( (-2, 0) \) to \( (0, 0) \).
- Draw a straight line from \( (0, 0) \) to \( (2, 4) \).

The final graph will have a horizontal segment on the x-axis from \( x = -2 \) to \( x = 0 \) and a line segment from \( (0, 0) \) to \( (2, 4) \).