The function shown in the image is $y = |x + 5|$, which represents an absolute value function. Here's how to approach graphing it:

Steps to Graph $y = |x + 5|$:

1. Understand the absolute value transformation:

   • The basic form of an absolute value function is $y = |x|$, which creates a "V"-shaped graph with the vertex at the origin (0, 0).
   • In $y = |x + 5|$, the graph is shifted horizontally by 5 units to the left. This shift is due to the $+5$ inside the absolute value function. So the vertex of the graph will be at $(-5, 0)$.

2. Identify key points:

   • Vertex: $(-5, 0)$.
   • The graph opens upwards, as the absolute value function always outputs positive values for $y$.

3. Shape of the graph:

   • For $x < -5$, the function behaves like $y = -(x + 5)$ because the expression inside the absolute value is negative.
   • For $x \geq -5$, the function behaves like $y = x + 5$.

4. Draw key points:

   • Plot the vertex at $(-5, 0)$.
   • Plot additional points on either side of the vertex, such as $(-6, 1)$ and $(-4, 1)$, and connect them to form the "V" shape.

5. Symmetry:

   • The graph is symmetric around the vertical line $x = -5$.

Would you like to see a plotted graph of this function, or do you need more details on the steps?

Related Questions:

1. How do you determine the domain and range of an absolute value function?
2. What happens to the graph of $y = |x + 5|$ if the constant inside changes (e.g., $|x - 5|$)?
3. How does multiplying an absolute value function by a constant (e.g., $y = 2|x + 5|$) affect its graph?
4. What is the difference between horizontal and vertical shifts in absolute value functions?
5. How can you graph the inverse of an absolute value function?

Tip: When graphing functions, it's useful to first identify any shifts (horizontal or vertical) from the base function, as this simplifies the graphing process.