Question

Identify the transformations, in order:

f(x) = -√x+1 +2
1) Translate left 3
2) Vertically shrink by factor 1/2
3) Vertical reflection
4) Translate 1 unit down

Answer 1

The transformations applied to the function f(x) = -√x+1 +2 are, in order: a 3-unit horizontal translation to the left, a vertical shrink by a factor of 1/2, a vertical reflection, and a 1-unit downward translation.

Step-by-step explanation:

To identify the transformations applied to the function f(x) = -√x+1 +2 in order, we must carefully analyze and apply each given transformation step by step:

1. Translate left 3 units: This moves the graph of the function 3 units to the left along the x-axis. If 'h' represents the horizontal shift, the new function becomes f(x) = -√(x+3)+1 +2.
2. Vertically shrink by factor 1/2: This scales the graph of the function down by a factor of 1/2 in the y-direction. This means each y-value is halved. The new function becomes f(x) = -√(x+3)/2 +2.
3. Vertical reflection: This flips the graph over the x-axis, changing the sign of the y-values. The new function now is f(x) = √(x+3)/2 +2.
4. Translate 1 unit down: This final transformation moves our function down by 1 unit in the y-direction. The completely transformed function looks like f(x) = √(x+3)/2 +1.

Remember to always check the math to make sure that these transformations have been applied correctly.