Which of the following equations could be for this cubic function?

Question

BlackTom AI · Accepted Answer

The question asks which equation could represent this cubic function. Here are the options to consider:

Option 1: y = (x + 1)^3. This is a horizontal shift of the basic cubic y = x^3 by -1 unit (the graph moves left). Cubic functions keep their characteristic S-shape (though shifted), so this form is a valid cubic.

Option 2: y = x^3 − 1. This is the basic cubic y = x^3 shifted downward by 1 unit. It remains a cubic with the same general shape as y = x^3, just translated.

Option 3: y = x^3 + 1. This is the basic cubic y = x^3 shifted upward by 1 unit. It also preserves the cubic shape and is a valid cubic function.

Option 4: y = (x − 1)^3. This is a horizontal shift of y = x^3 by +1 unit (the graph moves right). Like the others, it remains a cubic function.

Across all four options, each expression represents a cubic function, merely differing by horizontal or vertical shifts. A cubic function can be shifted in various ways and still be a cubic; the key is the x^3 term governs the overall shape, and all four forms retain that x^3 term albeit with shifts.

If you compare these forms to a baseline cubic, you’ll notice that shifts do not change the fundamental cubic nature, only the position of the graph. Therefore, all four options could, in principle, represent a cubic function depending on the shift, but the specific problem statement may have indicated a particular form. In this particular set, the first option is one valid cubic, as are the other three; the distinction would come from additional context about the graph’s location or intercepts.

Which of the following equations could be for this cubic function? 单项选择题

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