Question

Graph this function:
y=|x+3|

Answer 1

generate a visual representation

Answer 2

To graph the function \( y = |x + 3| \), follow these steps:

1. **Understand the Absolute Value Function**: The function \( y = |x + 3| \) represents a V-shaped graph that opens upward. The vertex of this graph occurs where the expression inside the absolute value is zero.

2. **Find the Vertex**: Set the expression inside the absolute value to zero:
\[
x + 3 = 0 \implies x = -3
\]
The vertex of the graph is at the point \((-3, 0)\).

3. **Determine Characteristics of the Graph**:
- For values of \( x < -3 \): \( y = -(x + 3) = -x - 3 \)
- For values of \( x \geq -3 \): \( y = x + 3 \)

4. **Calculate Points for Graphing**:
- When \( x = -5 \):
\[
y = |-5 + 3| = |-2| = 2 \quad \Rightarrow \quad (-5, 2)
\]
- When \( x = -4 \):
\[
y = |-4 + 3| = |-1| = 1 \quad \Rightarrow \quad (-4, 1)
\]
- When \( x = -3 \):
\[
y = |-3 + 3| = |0| = 0 \quad \Rightarrow \quad (-3, 0)
\]
- When \( x = -2 \):
\[
y = |-2 + 3| = |1| = 1 \quad \Rightarrow \quad (-2, 1)
\]
- When \( x = -1 \):
\[
y = |-1 + 3| = |2| = 2 \quad \Rightarrow \quad (-1, 2)
\]

5. **Plot the Points**: Plot the following points on a graph:
- (-5, 2)
- (-4, 1)
- (-3, 0) (vertex)
- (-2, 1)
- (-1, 2)

6. **Draw the V-Shape**: Connect the points to form a V shape, where the left arm decreases as \( x \) moves left from -3, and the right arm increases as \( x \) moves right from -3.

### Summary of the Graph
- The graph of the function \( y = |x + 3| \) has its vertex at the point (-3, 0).
- The left side of the V descends from (-3, 0) to the left, and the right side ascends from (-3, 0) to the right.

If you want me to generate a visual representation, please let me know!