To describe transformations of a graph mathematically, we adjust the equation of the graph based on the given transformations. Let's assume the original graph has an equation $y = f(x)$. Here's how each transformation is applied:

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(a) Shifting 6 units upward:

When a graph is shifted upward by $k$ units, we add $k$ to the function. The resulting equation becomes: $y = f(x) + 6$

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(b) Shifting 7 units to the right:

When a graph is shifted to the right by $h$ units, we replace $x$ with $x - h$ in the function. The resulting equation becomes: $y = f(x - 7)$

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(c) Reflecting about the y-axis:

When a graph is reflected about the y-axis, we replace $x$ with $-x$ in the function. The resulting equation becomes: $y = f(-x)$

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If you provide the specific function $f(x)$, I can rewrite these transformations explicitly for the given equation.

Would you like more details or examples for these transformations? Here are five questions that expand on this topic:

1. How would the equation change for a downward shift instead of upward?
2. What happens if you combine a vertical shift with a horizontal shift?
3. How does reflecting about the x-axis differ from reflecting about the y-axis?
4. Can you describe what happens graphically when shifting left instead of right?
5. How would the equation change if you stretched or compressed the graph vertically?

Tip: Always perform horizontal transformations (like shifting or reflecting) inside the parentheses of the function, and vertical transformations outside the function.