Let f(x)=x−2x2−4 . <IMAGE> Calculate f(x) for each value of x in the following table.
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1
First, let's simplify the function . Notice that the numerator can be factored as a difference of squares: .
Rewrite the function using the factored form: .
Observe that the terms in the numerator and the denominator can be canceled out, but only for to avoid division by zero. Thus, for .
Now, for each value of in the table, substitute into the simplified function to find the corresponding value of .
Remember to handle the case where separately, as the original function is undefined at this point due to division by zero. Consider the limit as approaches 2 if needed.
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