To determine which statement is true about the expressions based on Ella's work, we need to consider the criteria for equivalence of expressions. Two expressions are equivalent if they yield the same result for all values substituted into them.
The statements can be evaluated as follows:
A. The expressions are equivalent because Ella got different results when she substituted zero for f.
- This is incorrect. If the results are different when substituting the same value (zero), then the expressions are not equivalent.
B. The expressions are not equivalent because Ella would get the same results when substituting different numbers for f.
- This is incorrect wording. If they produce the same results for different inputs, that could suggest they are equivalent, not the opposite.
C. The expressions are equivalent because Ella got the same result when she substituted zero for f.
- This statement suggests that the expressions are equivalent based on a single substitution. However, for full equivalence, they need to provide the same result for all inputs, not just zero.
D. The expressions are not equivalent because Ella would get different results when substituting different numbers for f.
- This statement highlights that if Ella indeed got different results for different substituted values, then the expressions are not equivalent.
Given this evaluation, the most accurate option based on conventional logic regarding expression equivalence is D: The expressions are not equivalent because Ella would get different results when substituting different numbers for f.
Thus, the answer is D.
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