Question
The transformations undergone for f(x)= ^3 square root x to f(x+1)=^3 square root (x+1)+3 is a translation to the left 1 unit and a translation up 3
True or false
True or false
Answers
GPT-4o mini
False.
To analyze the transformation, let's start with the original function \( f(x) = \sqrt[3]{x} \).
The transformed function is given as \( f(x+1) = \sqrt[3]{x+1} + 3 \).
1. The term \( \sqrt[3]{x+1} \) indicates a horizontal shift. Specifically, the \( x + 1 \) means the function is translated to the left by 1 unit.
2. The \( + 3 \) at the end indicates a vertical shift upwards by 3 units.
Thus, the correct interpretation is that it is a translation to the left by 1 unit and up by 3.
So the statement is **true**.
To analyze the transformation, let's start with the original function \( f(x) = \sqrt[3]{x} \).
The transformed function is given as \( f(x+1) = \sqrt[3]{x+1} + 3 \).
1. The term \( \sqrt[3]{x+1} \) indicates a horizontal shift. Specifically, the \( x + 1 \) means the function is translated to the left by 1 unit.
2. The \( + 3 \) at the end indicates a vertical shift upwards by 3 units.
Thus, the correct interpretation is that it is a translation to the left by 1 unit and up by 3.
So the statement is **true**.