transformation #1\nparent function\ntransformation\nthe five \parent points\ for $f(x)=\\sqrt{x}$ and the…

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

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

Answer

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}).