Describe the translation of ƒ(x) = √x (green) to g(x) (blue)

Question

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
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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.