Question

find the function that is finally graphed after the following transformations are applied to the graph of \\(y = \sqrt{x}\\) in the order listed.

(1) reflect about the x-axis
(2) shift down 5 units
(3) shift right 5 units

Explanation:

Reflect about the x-axis

Using the Function Transformation knowledge point

$$ y_1 = -\sqrt{x} $$

Shift down 6 units

Using the Function Transformation knowledge point

$$ y_2 = -\sqrt{x} - 6 $$

Shift right 5 units

Using the Function Transformation knowledge point

$$ y_3 = -\sqrt{x - 5} - 6 $$

Answer:

\(y = -\sqrt{x - 5} - 6\)