Use the image to answer the question.

To determine the equation of the cube root function that Sam graphed, let's analyze the provided options.

A cube root function typically has the form:

\[ y = a \sqrt[3]{x - h} + k \]

where \( (h, k) \) represents the horizontal and vertical shifts, respectively, and \( a \) represents a vertical scaling factor.

The provided options are:

1. \( y = 2 \sqrt[3]{x - 1} + 3 \)
2. \( y = \sqrt[3]{x - 1} + 3 \)
3. \( y = 2 \sqrt[3]{x + 1} - 3 \)
4. \( y = \sqrt[3]{x + 1} - 3 \)

Without the image, we can't directly observe the curve's characteristics, but we generally can determine the shifts.

- If the graph appears to shift right by 1 and up by 3, the appropriate equation would be \( y = \sqrt[3]{x - 1} + 3 \).
- If it appears more stretched or compressed vertically, we may need to consider the \( a \) coefficient from the first or third option.
- A downward shift of 3 would indicate either the third or fourth options.

To summarize, without the visual context but based on the standard cubic root transformation characteristics, I would recommend checking for whether the graph has shifts and identifies the axis intersecting points.

If the function is intended to be shifted to the right by 1 and up by 3, then the correct answer would be:

**\(y = \sqrt[3]{x - 1} + 3\)** which is option 2.

Make sure to validate this against the characteristics of the graph presented in the image.