The function h(x) = (x – 3)3 + 1 is graphed on a coordinate grid. Which statements about the graph are true? Check all that apply.The domain of the function is all real numbers.The range of the function is all real numbers.The graph is a translation 3 left and 1 up from the function f(x) = x3.The graph crosses the y-axis once.The graph crosses the x-axis three times.The graph increases from negative infinity to positive infinity.

A cubic function is defined for every real x, and its outputs cover all real numbers, so the domain and range are both all real numbers. The graph is shifted 3 units right and 1 unit up from y = x³, not 3 units left. It crosses the y-axis once, at x = 0, and crosses the x-axis where (x − 3)³ + 1 = 0, which gives x = 2, so it does not cross three times. Since a cubic remains increasing after these shifts, it increases from negative infinity to positive infinity.

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