Consider the equation f(x)= -2 sqrt(X+3).
List in order the transformations applied to the parent function.
To determine the transformations applied to the parent function, we need to analyze the given equation:
f(x) = -2√(x + 3).
The parent function is the square root function, f(x) = √x. Here are the transformations applied to the parent function in order:
1. Horizontal shift: The expression (x + 3) inside the square root represents a shift of 3 units to the left. This means the graph will be shifted 3 units to the left compared to the parent function since x values are subtracted by 3.
2. Vertical reflection: The negative sign in front of the entire expression (-2√(x + 3)) reflects the graph vertically. This means the graph will be mirrored (flipped) over the x-axis.
3. Vertical stretch/compression: The coefficient 2 in front of the square root function (-2√(x + 3)) indicates a vertical stretch/compression. Since the coefficient is 2, the graph will be compressed vertically by a factor of 2. If the coefficient were greater than 1, it would indicate a vertical stretch, and if it were between 0 and 1, it would indicate a vertical compression.
So, in summary, the transformations applied to the parent function f(x) = √x are a horizontal shift 3 units to the left, a vertical reflection (flipped) over the x-axis, and a vertical compression by a factor of 2.