The equation you have written is:

$y = |x + 3|$

This represents an absolute value function. In this case, the function is defined as the absolute value of $x + 3$.

How it works:

• Absolute value means that the expression inside the absolute value signs will always be non-negative. If the expression $x + 3$ is positive, it remains as it is; if it's negative, it becomes positive (its opposite).
• So, $y = |x + 3|$ means that for any value of $x$, $y$ will be the distance of $x + 3$ from zero on the number line.

Key features of this graph:

1. Vertex: The vertex of this function is at $x = -3$, where the expression inside the absolute value becomes zero. Therefore, the point $(-3, 0)$ is the vertex of the graph.
2. Shape: The graph of this function will be a "V" shape, opening upwards, with the vertex at $(-3, 0)$.
3. Symmetry: The graph is symmetric about the vertical line $x = -3$.

Would you like further clarification on how to graph this or any other part of the function? Feel free to ask!

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5 Follow-Up Questions:

1. How would the graph change if the equation was $y = |x - 3|$?
2. What happens if we add a constant, like $y = |x + 3| + 2$?
3. Can you explain how to solve for $x$ when $y = |x + 3|$?
4. How do absolute value equations behave when combined with linear equations?
5. How can we determine if a function is one-to-one?

Tip:

Remember that the absolute value function is a piecewise function. For $y = |x + 3|$, it can be rewritten as:

\begin{cases} x + 3 & \text{if } x \geq -3 \\ -(x + 3) & \text{if } x < -3 \end{cases}$$