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
Option 1: t(x) = x³- 2
Option 2: m(x) = x²
Option 3: z(x) = 2x
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Answered by
GPT-4o mini
To determine which function is a transformation of \( f(x) = x^3 \), we need to analyze the given options:
1. **Option 1: \( t(x) = x^3 - 2 \)**
This function involves the original function \( f(x) = x^3 \) with a vertical shift downward by 2 units. Therefore, it is a transformation of \( f(x) \).
2. **Option 2: \( m(x) = x^2 \)**
This function is a different type of function (a quadratic function) and does not represent a transformation of \( f(x) = x^3 \).
3. **Option 3: \( z(x) = 2x \)**
This function is a linear transformation and does not correspond to \( f(x) = x^3 \).
Based on the analysis above, the function that is a transformation of the function \( f(x) = x^3 \) is:
**Option 1: \( t(x) = x^3 - 2 \)**.
1. **Option 1: \( t(x) = x^3 - 2 \)**
This function involves the original function \( f(x) = x^3 \) with a vertical shift downward by 2 units. Therefore, it is a transformation of \( f(x) \).
2. **Option 2: \( m(x) = x^2 \)**
This function is a different type of function (a quadratic function) and does not represent a transformation of \( f(x) = x^3 \).
3. **Option 3: \( z(x) = 2x \)**
This function is a linear transformation and does not correspond to \( f(x) = x^3 \).
Based on the analysis above, the function that is a transformation of the function \( f(x) = x^3 \) is:
**Option 1: \( t(x) = x^3 - 2 \)**.
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