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

Question

True or false

Answer 1

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.