To represent the translation of Ella's hexagon 7 units to the left, we need to understand how translations of functions work.
- If we have a function \( f(x) \) that represents the coordinates of the hexagon, shifting it 7 units to the left means we replace \( x \) with \( x + 7 \). This is because to shift left, we need to add to the input (since the graph moves left in the coordinate plane when inputs become larger).
So, the translated function \( g(x) \) can be expressed as: \[ g(x) = f(x + 7) \]
Looking at the options you provided, the correct representation for the translation 7 units to the left would be \( g(x) = f(x + 7) \).
However, since this exact notation isn't provided, let's break down the options you listed:
- \( 0f(2) = 2 - 7 \) doesn't seem correct in terms of notation.
- \( f(x) = x \) suggests a linear function, but it does not show the translation.
- \( 0f(a) = 2 + 7 \) suggests an incorrect input notation.
- \( 0g(3) = 3 - ? \) is incomplete.
None of the options specifically show the correct transformation for shifting 7 units left. Instead, for \( f(x) \), the correct transformation expressing the leftward shift in general terms would be represented by:
\[ g(x) = f(x + 7) \]
If you have to pick one from the provided options that reflects the idea of input change for the translation left, The expression can be likely interpreted from these could have been written incorrectly or is misunderstood in context.
To summarize: Ella would represent the translation function as \( g(x) = f(x + 7) \) for shifting her hexagon 7 units to the left, but that specific notation wasn't listed in your options.