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Use the image to answer the question.

An s-shaped curve is plotted on a coordinate plane. Both axes range from 0 to 5 in increments of 1.

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 minus 1 End Root plus 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
y equals root index 3 Start Root x plus 1 End Root minus 3
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1 answer

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.