Question

The graph of the parent function f(x) = x3 is transformed such that . Which statements about the graph of g(x) are accurate? Select three options.

The graph does not pass through the origin.
As x approaches negative infinity, the graph of g(x) approaches infinity.
As x approaches infinity, the graph of g(x) approaches infinity.
The domain of the function is all real numbers.
The range of the function is all real numbers.

Answer 1

Assuming the transformation is a vertical stretch g(x) = 2x^3 (a common missing detail), the three accurate statements are:

- As x approaches infinity, the graph of g(x) approaches infinity.
- The domain of the function is all real numbers.
- The range of the function is all real numbers.

Reason: g(0)=0 so it still passes through the origin (so "does not pass through the origin" is false). As x→−∞, 2x^3→−∞, not ∞. The cubic (any nonconstant odd-degree polynomial) has domain and range all reals and with positive leading coefficient its right end goes to ∞.