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The problem asks to find a function that describes the graph shown, which is a vertical shift of the basic function \( y = \sqrt[3]{x} \).

### Step-by-step approach:

1. **Basic function**: The unshifted function is \( y = \sqrt[3]{x} \), which describes a cube root function.
2. **Vertical shift**: Looking at the graph, the entire graph has been shifted upward. From the point (0, 0) in the original function, we now see the graph passing through the point (0, 3). This suggests a vertical shift of 3 units upward.
3. **Resulting function**: A vertical shift of 3 units upward means we add 3 to the basic function.

Thus, the function that describes the graph is:
\[
f(x) = \sqrt[3]{x} + 3
\]

Would you like further details or clarification? Here are some related questions:

1. What are the properties of cube root functions, and how do they change with vertical shifts?
2. How would the graph change if the shift was downward instead of upward?
3. Can horizontal shifts be combined with vertical shifts for cube root functions?
4. How does the domain and range of the function change with the shift?
5. How would you express this function in terms of transformations of parent functions?

**Tip**: When identifying vertical shifts, always look at how key points on the graph move relative to the original function.

The graph to the right was created by vertically shifting the graph of the basic function y = ∛x. Write a function that describes the graph to the right.

This problem involves a vertical shift of the basic cube root function y = ∛x. The graph shows a shift of 3 units upward, resulting in the function f(x) = ∛x + 3. Ideal for high school students in Grades 9-12.

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