Describe the transformations for the equation below compared to the parent function y = x^3.
y = -1/2(x+4)^3 - 1
The given equation, y = -1/2(x+4)^3 - 1, is a transformation of the parent function y = x^3.
Transformation 1: Horizontal translation to the left by 4 units.
The term (x+4) inside the parentheses represents a horizontal shift of 4 units to the left compared to the parent function.
Transformation 2: Vertical reflection.
The negative sign in front of the equation (-1/2) reflects the graph vertically compared to the parent function. This means that the graph is inverted or flipped over the x-axis.
Transformation 3: Vertical compression by a factor of 1/2.
The coefficient of -1/2 shrinks the graph of the parent function vertically by a factor of 1/2. This makes the graph narrower compared to the parent function.
Transformation 4: Vertical translation downward by 1 unit.
The constant term -1 shifts the graph downward by 1 unit compared to the parent function.