Question

1. create a square root function that has a translation 3 units to the right and 4 units down, with a vertical stretch of 3, and a reflection over the x-axis.

Explanation:

⚡ Using what you learned: combining transformations

Step 1: Identify the parent function

The parent square root function is:

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

Step 2: Apply the transformations

• Reflection over the x-axis: Multiply the function by \(-1\).
• Vertical stretch of 3: Multiply the function by \(3\).
• Translation 3 units to the right: Replace \(x\) with \(x - 3\).
• Translation 4 units down: Subtract \(4\) from the entire function.

Combining these transformations into the general form \(g(x) = a\sqrt{x - h} + k\):

$$ a = -3 $$

$$ h = 3 $$

$$ k = -4 $$

Step 3: Write the final equation

$$ g(x) = -3\sqrt{x - 3} - 4 $$

Answer:

$$ g(x) = -3\sqrt{x - 3} - 4 $$