Question

transformation #1
parent function
transformation
the five \parent points\ for $f(x)=\sqrt{x}$ and the corresponding transformed points for our function $f(x)=\sqrt{x}-2$ are shown.
notice that the x - coordinates didnt change.
how did the y - coordinates change? be as specific as you can.

Explanation:

Step1: Analyze the first pair of points

For the first pair \((0,0)\) (parent function) and \((0, - 2)\) (transformed function). The change in \(y\) - coordinate is \(-2-0=-2\).

Step2: Analyze the second pair of points

For the second pair \((1,1)\) (parent function) and \((1,-1)\) (transformed function). The change in \(y\) - coordinate is \(-1 - 1=-2\).

Step3: Analyze the third pair of points

For the third pair \((4,2)\) (parent function) and \((4,0)\) (transformed function). The change in \(y\) - coordinate is \(0 - 2=-2\).

Step4: Analyze the fourth pair of points

For the fourth pair \((9,3)\) (parent function) and \((9,1)\) (transformed function). The change in \(y\) - coordinate is \(1 - 3=-2\).

Step5: Analyze the fifth pair of points

For the fifth pair \((16,4)\) (parent function) and \((16,2)\) (transformed function). The change in \(y\) - coordinate is \(2 - 4=-2\).

Answer:

The \(y\) - coordinates of the points of the function \(y = \sqrt{x}-2\) are obtained by subtracting \(2\) from the \(y\) - coordinates of the points of the parent function \(y=\sqrt{x}\).