Let g(x)=8∣x−2∣x3−4x. <IMAGE> Calculate g(x) for each value of x in the following table.
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Identify the function given: . This function involves a polynomial in the numerator and an absolute value in the denominator.
Understand the absolute value function: means that the expression inside the absolute value will be positive regardless of the sign of . This affects the domain and behavior of the function.
For each value of provided in the table, substitute into the function . This involves calculating for the numerator and for the denominator.
Simplify the expression for each by performing the arithmetic operations: calculate the cube and linear terms in the numerator, and evaluate the absolute value in the denominator.
Ensure that the denominator is not zero for any value, as this would make the function undefined. If , the denominator becomes zero, so check for this condition and handle it appropriately.
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