In the image, we have a graph with two curves: a black one labeled as $y = f(x)$ and a red one for which the equation is to be determined. The instructions mention the "big idea of opposites," which suggests that this question is about transformations of the function $f(x)$.

Looking at the options and the visual clues:

1. The red graph appears to be a reflection of the black graph across the y-axis. This is a typical transformation that occurs when we replace $x$ with $-x$ in the function's argument, i.e., $y = f(-x)$.

Now, let's match this concept with the choices:

• Option A: $y = f(x/(-1))$ — This is equivalent to $y = f(-x)$, which fits the description of a reflection across the y-axis.
• Option B: $y - 1 = f(x)$ — This describes a vertical shift down by 1 unit, which doesn't match the reflection.
• Option C: $y = f(x - 1)$ — This describes a horizontal shift to the right by 1 unit, not a reflection.
• Option D: $y(-1) = f(x)$ — This is unclear and does not match any standard transformation notation.

Thus, Option A: $y = f(x/(-1))$ is the correct equation for the red graph, representing the reflection of $f(x)$ across the y-axis.

Would you like further details or have any questions?

Here are 5 related questions to consider:

1. How does changing $f(x)$ to $f(-x)$ affect the graph?
2. What is the difference between reflecting across the y-axis and reflecting across the x-axis?
3. What happens to the graph when you apply a vertical or horizontal shift?
4. Can you explain the effect of stretching or compressing a graph using scaling transformations?
5. What transformation is represented by $y = -f(x)$?

Tip: Always consider how modifying $x$ or $y$ inside or outside the function affects the graph's shape or position.