Yes, when graphing the function $h(x) = -|x - 6| + 3$, the value 6 inside the absolute value function corresponds to a horizontal shift. Specifically, it shifts the graph 6 units to the right, making $x = 6$ the point of symmetry or the vertex.

Here’s how it breaks down:

1. Equation breakdown:

   • The equation $h(x) = -|x - 6| + 3$ is in the form $h(x) = -|x - h| + k$.
   • $h = 6$, which shifts the graph 6 units to the right.
   • $k = 3$, which shifts the graph 3 units upwards.

2. Vertex:

   • The vertex of the graph will be at $(6, 3)$.

3. Reflection:

   • The negative sign in front of the absolute value indicates a reflection across the x-axis. So instead of the usual V-shape opening upwards, the graph will open downwards.

In conclusion, the 6 inside $|x - 6|$ does indicate a horizontal shift to the right, making it a positive shift, while the graph opens downward due to the negative sign in front of the absolute value.

Would you like to see the graph of this function?

Related Questions:

1. How would the graph change if the equation were $h(x) = |x - 6| + 3$ (without the negative sign)?
2. What is the effect of changing the value of $k$ in the equation $h(x) = -|x - 6| + k$?
3. How does the reflection across the x-axis affect the vertex form of the absolute value function?
4. How can you find the range of the function $h(x) = -|x - 6| + 3$?
5. What happens if you change the 6 to a negative value, say $h(x) = -|x + 6| + 3$?

Tip:

The horizontal shift is always opposite in sign to the value inside the absolute value. If you see $x - 6$, it means a shift to the right by 6 units.