Question

write the equation of a function that has the given characteristics.

the graph of \\(y = \sqrt{x}\\), shifted 6 units downward

a. \\(y = \sqrt{x+6}\\)
b. \\(y = \sqrt{x}-6\\)
c. \\(y = \sqrt{x-6}\\)
d. \\(y = \sqrt{x}+6\\)

Explanation:

Identify the parent function

Using the Function Transformation knowledge point

$$ f(x) = \sqrt{x} $$

Apply the vertical shift transformation

Using the Function Transformation knowledge point

$$ g(x) = f(x) - 6 = \sqrt{x} - 6 $$

Match with the given options

Using the Function Transformation knowledge point

$$ y = \sqrt{x} - 6 \implies \text{Option B} $$

Answer:

• (A) \(y = \sqrt{x+6}\)
• (B) \(y = \sqrt{x}-6\) (Correct answer)
• (C) \(y = \sqrt{x-6}\)
• (D) \(y = \sqrt{x}+6\)