Question

Which function is a transformation of the parent function f(x)=x3
?

Option #1: g(x)=3x


Option #2: h(x)=x3+3


Option #3: j(x)=x2

Answer 1

To determine which function is a transformation of the parent function \( f(x) = x^3 \), let's analyze the given options:

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

2. \( h(x) = x^3 + 3 \): This represents a vertical transformation of the function \( f(x) = x^3 \). Specifically, it shifts the graph of \( f(x) \) upwards by 3 units. Thus, \( h(x) \) is indeed a transformation of the parent function.

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

Based on this analysis, the correct answer indicating a transformation of the parent function \( f(x) = x^3 \) is:

**Option #2: \( h(x) = x^3 + 3 \)**.