Question

Sam graphed a cube root function. What is the equation of the function Sam graphed? (1 point) Responses y=2x−1−−−−−√3+3 y equals 2 root index 3 Start Root x minus 1 End Root plus 3 y=x+1−−−−−√3−3 y equals root index 3 Start Root x plus 1 End Root minus 3 y=2x+1−−−−−√3−3 y equals 2 root index 3 Start Root x plus 1 End Root minus 3 y=x−1−−−−−√3+3

Answer 1

To identify the correct equation of the cube root function Sam graphed, we should look for the general form of a cube root function, which can be expressed as:

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

where:
- \( a \) is a vertical stretch/compression factor,
- \( (h, k) \) is the translation of the graph.

From the options given, let's analyze each one:

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

Since there is no additional context about transformations or specific points, all we can conclude is que the correct format is comparable to the original base cube root structure.

### Looking at the options:
1. **First Option**: Translation right by 1 unit, vertical stretch by 2, translation up by 3.
2. **Second Option**: Translation left by 1 unit and translation down by 3 units.
3. **Third Option**: Translation left by 1 unit, vertical stretch by 2, and translation down by 3 units.
4. **Fourth Option**: Translation right by 1 unit and translation up by 3.

Given all this analysis, the specific choice depends on Sam's graph. Without more details about the transformations (like which way it shifted or stretched), it is hard to pinpoint the correct answer.

If more context to the specific transformations is provided, we will then be able to accurately identify which function corresponds to Sam's graph.