In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 4)^3 + 6. The turning point of the graph is where the substance changes from a liquid to a gas. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function.
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The function T = x^3 has a turning point at x = 0. We can determine this simply by looking at the graph T = x^3. Therefore, (0,0) is the turning point for the graph T = x^3.
The function T(x) = (x - 4)^3 + 6 will be the graph T = x^3 shifted to the right by 4 units and shifted up by 6 units. Therefore, the turning point will also shift from (0,0) to 4 units to the right and 6 units up. The turning point will be (4,6) for the function T(x) = (x - 4)^3 + 6.
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