Consider the equation f(x)= -2 sqrt(X+3).
List in order the transformations applied to the parent function.
The equation f(x) = -2 sqrt(x+3) represents a transformation of the parent function f(x) = sqrt(x).
Here are the transformations applied to the parent function, in order:
1. Shift to the left by 3 units: The equation f(x) = -2 sqrt(x+3) represents a horizontal shift to the left by 3 units compared to the parent function f(x) = sqrt(x). The "+3" inside the square root means that the function x+3 is being evaluated first before taking the square root.
2. Vertical stretch: The equation f(x) = -2 sqrt(x+3) represents a vertical stretch by a factor of 2 compared to the parent function. The coefficient "-2" in front of the square root means that the function is being vertically stretched by a factor of 2.
3. Reflection about the x-axis: The negative sign in front of the equation "-2 sqrt(x+3)" indicates a reflection about the x-axis compared to the parent function.
So, the order of transformations applied to the parent function is:
1. Shift to the left by 3 units.
2. Vertical stretch by a factor of 2.
3. Reflection about the x-axis.
To determine the transformations applied to the parent function, we need to examine the given equation f(x) = -2 sqrt(x + 3) and compare it to the standard form of the parent function y = sqrt(x).
Let's break it down step by step:
1. Vertical Transformation:
The negative sign in front of the equation, -2, indicates a reflection across the x-axis. This means the graph is flipped vertically.
2. Horizontal Transformation:
The term inside the square root function, (x + 3), represents a horizontal shift of 3 units to the left. Since it is x + 3, we shift it in the opposite direction by 3 units to the left.
3. Vertical Scaling:
The coefficient in front of the square root function, -2, represents a vertical scaling or stretching. In this case, it compresses the graph vertically by a factor of 2.
To summarize, the transformations applied to the parent function y = sqrt(x) are:
1. Vertical reflection (flipped vertically)
2. Horizontal shift 3 units to the left
3. Vertical compression by a factor of 2.
Therefore, the transformations in order are: vertical reflection, horizontal shift left 3 units, vertical compression by a factor of 2.
shift 3 left
scale by 2 vertically
reflect in x-axis
In this case, the order does not really matter. Try them and see.