Question

Examine the transformation of the parent function f(x) = √x. Identify the three transformations and describe them in words.

Answer 1

The transformation of the parent function f(x) = √x involves a vertical shift, a horizontal shift, and a vertical stretch or compression.

Step-by-step explanation:

The parent function of f(x) = √x is the square root function. The transformation of this parent function involves three main changes:

1. Vertical Shift: The function is shifted vertically up or down.
2. Horizontal Shift: The function is shifted horizontally left or right.
3. Vertical Stretch or Compression: The function is stretched or compressed vertically.

Each of these transformations can be achieved using the following equations:

• Vertical Shift: f(x) = √(x - h) + k
• Horizontal Shift: f(x) = √(x - h) + k
• Vertical Stretch or Compression: f(x) = a√(x - h) + k

Where h represents the horizontal shift, k represents the vertical shift, and a represents the vertical stretch or compression.