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) shift down 9 units
(2) reflect about the x-axis
(3) reflect about the y-axis

Explanation:

Identify the parent function

Using the Function Transformation knowledge point

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

Apply the vertical shift

Using the Function Transformation knowledge point

$$ y_1 = f(x) - 9 = \sqrt{x} - 9 $$

Apply the reflection about the x-axis

Using the Function Transformation knowledge point

$$ y_2 = -y_1 = -(\sqrt{x} - 9) = -\sqrt{x} + 9 $$

Apply the reflection about the y-axis

Using the Function Transformation knowledge point

$$ y_3 = -\sqrt{-x} + 9 $$

Answer:

\(y = -\sqrt{-x} + 9\)