Question

Describe the translation of ƒ(x) = √x (green) to g(x) (blue)
A horizontal shift is a translation moves along the x-axis. **To find the direction of the translation, set the transformation expression (within parenthesis) equal to zero and solve. The result will always give your the magnitude and direction of the translation
*
1 point

g(x) = √(x+2)
g(x) = √(x-2)

Answer 1

To analyze the translation of the function \( f(x) = \sqrt{x} \) to \( g(x) \), we can look at the transformations involved based on the expressions given.

1. **For \( g(x) = \sqrt{x + 2} \)**:
- We can set the transformation expression \( x + 2 \) to zero and solve for \( x \):
\[
x + 2 = 0 \implies x = -2
\]
- This result indicates a horizontal shift to the **left** by 2 units. Therefore, the transformation from \( f(x) = \sqrt{x} \) to \( g(x) = \sqrt{x + 2} \) represents a translation of the original function 2 units to the left.

2. **For \( g(x) = \sqrt{x - 2} \)**:
- Similarly, we can set the transformation expression \( x - 2 \) to zero and solve for \( x \):
\[
x - 2 = 0 \implies x = 2
\]
- This result indicates a horizontal shift to the **right** by 2 units. Therefore, the transformation from \( f(x) = \sqrt{x} \) to \( g(x) = \sqrt{x - 2} \) represents a translation of the original function 2 units to the right.

In summary:
- For \( g(x) = \sqrt{x + 2} \), it's a horizontal shift **left** by 2 units.
- For \( g(x) = \sqrt{x - 2} \), it's a horizontal shift **right** by 2 units.