Question
Question 1:
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
Answers
GPT-4o mini
To identify which function is a transformation of \( f(x) = x^3 \), we need to look at each option:
1. **Option 1: \( t(x) = x^3 - 2 \)** - This is a vertical transformation of the original function \( f(x) = x^3 \). It shifts the graph of \( f(x) \) down by 2 units.
2. **Option 2: \( m(x) = x^2 \)** - This is a different function entirely (a quadratic function) and is not a transformation of \( f(x) = x^3 \).
3. **Option 3: \( z(x) = 2x \)** - This is also a different function (a linear function) and not a transformation of \( f(x) = x^3 \).
Based on this analysis, the correct answer is:
**Option 1: \( t(x) = x^3 - 2 \)**.
1. **Option 1: \( t(x) = x^3 - 2 \)** - This is a vertical transformation of the original function \( f(x) = x^3 \). It shifts the graph of \( f(x) \) down by 2 units.
2. **Option 2: \( m(x) = x^2 \)** - This is a different function entirely (a quadratic function) and is not a transformation of \( f(x) = x^3 \).
3. **Option 3: \( z(x) = 2x \)** - This is also a different function (a linear function) and not a transformation of \( f(x) = x^3 \).
Based on this analysis, the correct answer is:
**Option 1: \( t(x) = x^3 - 2 \)**.