Final answer:
g(x) = 3x² is different from f(x) = x² in that it is a steeper version of the f(x) parabola, although they both share the same shape. Both functions have the same domain of all real numbers, but the range for g(x) is vertically stretched due to the coefficient 3, which affects the output values.
Step-by-step explanation:
The function g(x) = 3x² differs from f(x) = x² in that g(x) is a steeper version of the f(x) parabola due to the coefficient 3, which stretches the parabola vertically. However, both functions have the same shape, as they are both parabolas, just with different steepness. The domain for both functions is all real numbers, as there are no restrictions on x for either function. The range for both functions is all real numbers greater than or equal to zero, since the squared term ensures all outputs will be non-negative. Therefore, the most accurate description is that they have the same shapes, but g(x) has a different range due to the vertical stretch.
Correct answer: Option C) Same shapes, different domain and range.