Question

Examine the transformation of the parent function f(x) = √x. Identify the three transformations and describe them in words for the function g(x) = 2/3√(-x + 1).

A) Horizontal reflection, vertical compression by a factor of 2/3, horizontal translation right by 1 unit.
B) Vertical reflection, horizontal compression by a factor of 2/3, horizontal translation left by 1 unit.
C) Horizontal reflection, vertical compression by a factor of 3/2, horizontal translation left by 1 unit.
D) Vertical reflection, horizontal compression by a factor of 3/2, horizontal translation right by 1 unit.

Answer 1

The three transformations for the function g(x) = 2/3√(-x + 1) are horizontal reflection, vertical compression by a factor of 2/3, and horizontal translation right by 1 unit.

Step-by-step explanation:

The three transformations for the function g(x) = 2/3√(-x + 1) are:

1. Horizontal reflection: The negative sign (-) in front of x indicates a reflection about the y-axis. This means that the graph is flipped horizontally.
2. Vertical compression by a factor of 2/3: The coefficient 2/3 in front of the square root symbol (√) indicates that the graph is compressed vertically.
3. Horizontal translation right by 1 unit: The +1 inside the square root symbol (√) indicates a horizontal translation to the right by 1 unit.