To determine the equation of the cube root function that Sam graphed, we need to look for key components in a typical cube root function format, which is generally expressed as:
\[ y = a \sqrt[3]{x - h} + k \]
where:
- \( a \) is a vertical stretch or compression,
- \( (h, k) \) is the point of translation (the horizontal and vertical shifts).
From the given options, the terms including cube root (\( \sqrt[3]{\cdot} \)) and constants indicate shifts and transformations of a base cube root function.
- y = 2√3(x + 1) - 3
- y = √3(x + 1) - 3
- y = √3(x - 1) + 3
- y = 2x - 1√3 + 3
Given the structure of these options, we should verify if there are any horizontal or vertical shifts, as well as any scalars affecting the slope of the cube root. Based on the transformations, we would evaluate how each component describes movement on the graph.
The correct response would follow the general cube root function's format. If more context on the graph is visible, especially concerning shifts and how steep the function appears, we could pinpoint the answer more accurately.
Without the image, it's challenging to choose definitively, but generally, the equation might look like one of the second or third options depending on if there's an upward or downward shift.
Please double-check the graph details to reflect on shifts and scalars to conclude accurately.
1 answer