Question

Use the image to answer the 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=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 y=x−1−−−−−√3+3

Answer 1

To determine the equation of the cube root function graphed by Sam, we need to consider the general form of a cube root function, which is typically expressed as:

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

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

From the provided answer choices, we need to identify the correct function based on likely transformations derived from standard forms.

Here are the characteristics you would look for:

- The function should be a cube root function, which includes the cube root symbol \(\sqrt[3]{\cdot}\).
- Look for shifts up or down (vertical) and left or right (horizontal) indicated by \(- h\) and \(+ k\).
- The coefficient \(a\) will stretch (if \(a > 1\)) or compress (if \(0 < a < 1\)) the graph vertically.

Without the image to analyze directly, I can't specify which one Sam graphed but here's how you can apply the reasoning:

1. **Identify the shifts**: If the graph has an intercept at a certain point above or below the y-axis, it will guide the values of \(h\) and \(k\).

2. **Scaling factor**: If the graph is noticeably steeper or flatter, look for those coefficients in front of \(\sqrt[3]{\cdot}\).

Once you have this information from the graph, you can match it to the choices provided. Based on your context, you'll look for a function that showcases both horizontal and vertical shifts, as well as a possible scaling adjustment.

Select the option that aligns best with the observed graph shifts and shape.