To identify the equation of the cube root function that Sam graphed, we need to analyze the structure of a typical cube root function and the transformations applied to it.
A standard cube root function can be written as:
\[ y = \sqrt[3]{x} \]
From the options provided, we see variations of this function with additional constants added to either the input or the output. The general form of the transformed cube root function can be expressed as:
\[ y = a \sqrt[3]{x - h} + k \]
Where:
- \( (h, k) \) indicates a horizontal and vertical shift.
- \( a \) represents a vertical stretch/compression.
Now let's look at the options closely:
- \( y = 2 \sqrt[3]{x + 1} - 3 \)
- \( y = 2 \sqrt[3]{x - 1} + 3 \)
- \( y = \sqrt[3]{x + 1} - 3 \)
- \( y = \sqrt[3]{x - 1} + 3 \)
To analyze these, we need to see how they shift from the base function \( y = \sqrt[3]{x} \):
- If there is a "+1" or "-1" inside the cube root, it indicates a left or right shift.
- If there is a "+3" or "-3" outside the cube root, it indicates an upward or downward shift.
Without additional context or a visual representation, it can be challenging to determine precisely which option corresponds to the s-shaped curve you mentioned. However, if we were to infer:
- If the curve shifts to the left and downward considerably, the likely candidate might be \( y = \sqrt[3]{x + 1} - 3 \) (Option 3).
Conversely, if it shifted right and up, then \( y = \sqrt[3]{x - 1} + 3 \) (Option 4) would be appropriate.
Since the question states that Sam graphed a cube root function, let's select the option that reflects a typical transformation while falling within common shifts observed:
Therefore, the answer based on typical attributes of cube root transformations would likely be:
y = \sqrt[3]{x - 1} + 3 (option 4)
Please validate based on any specific observations in the graph provided.
5 answers