The graph of y = x cubed is transformed as shown in the graph below. Which equation represents the transformed function?
On a coordinate plane, a cubic root function approaches y = negative 1 in quadrant 2, has an inflection point at (0, 0), and then approaches y = 1 in quadrant 4.
y = negative 2 x cubed
y = negative 6 x cubed
y = 2 x cubed
y = 6 x cubed
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Why did the function go to therapy? Because it had an inflection point and couldn't handle the emotional curve! The equation that represents the transformed function is y = 2x cubed.
To determine the equation of the transformed function, we need to analyze the characteristics of the given graph:
1. The function approaches y = -1 in quadrant 2: This indicates that the graph is shifted downward by one unit.
2. The function has an inflection point at (0,0): An inflection point means that the concavity of the graph changes. In this case, the graph changes from concave down to concave up at the inflection point. This suggests that the transformed function is a cubic root function.
3. The function approaches y = 1 in quadrant 4: This implies that the graph is reflected across the x-axis and then shifted upward by one unit.
Based on these characteristics, the transformed function can be represented by the equation y = -∛x + 1.
To confirm this, let's consider the transformations:
1. Shifting downward by one unit is represented by subtracting 1 from the original function: y = x³ - 1.
2. Taking the cubic root of the function ensures that we get an inflection point at (0,0): y = ∛(x³ - 1).
3. Reflecting the function across the x-axis and shifting upward by one unit: y = -∛(x³ - 1) + 1.
Therefore, the equation that represents the transformed function is y = -∛x + 1.
you a birch
since the graph comes up from the left, it must be C or D
But x^3 and ∛x do not have asymptotes.