Question

Which function is a transformation of the parent function f(x) = x^3
g(x)=3x
h(x)=x^3+3
j(x)=x^2

Answer 1

To determine which function is a transformation of the parent function \( f(x) = x^3 \), we need to analyze each option:

1. **\( g(x) = 3x \)**: This is a linear function and not a transformation of the cubic function.

2. **\( h(x) = x^3 + 3 \)**: This function represents a vertical shift of the parent function \( f(x) = x^3 \) upwards by 3 units. Therefore, \( h(x) \) is a transformation of \( f(x) \).

3. **\( j(x) = x^2 \)**: This is a quadratic function and therefore not a transformation of the cubic function.

Among the options, the function that is a transformation of the parent function \( f(x) = x^3 \) is \( h(x) = x^3 + 3 \).