Question

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

Option 1: t(x) = x³- 2
Option 2: m(x) = x²
Option 3: z(x) = 2x

Answer 1

To determine which of the given functions is a transformation of the function \( f(x) = x^3 \), we need to look for functions that can be derived from \( f(x) \) through transformations such as translations, stretches, or reflections.

1. **Option 1: \( t(x) = x^3 - 2 \)**
This function is a vertical translation of \( f(x) = x^3 \) downward by 2 units. It retains the cubic form, so it is indeed a transformation of \( f(x) \).

2. **Option 2: \( m(x) = x^2 \)**
This function changes the degree of the polynomial from cubic \( (x^3) \) to quadratic \( (x^2) \). Therefore, it is not a transformation of \( f(x) \).

3. **Option 3: \( z(x) = 2x \)**
This function is a linear function (a degree 1 polynomial) and does not maintain the cubic nature of \( f(x) = x^3 \). So, it is also not a transformation of \( f(x) \).

Based on this analysis, the correct answer is:

**Option 1: \( t(x) = x^3 - 2 \)**