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:
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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 \(k\).
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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.
1 answer