Questions: Please print your full name in capital letters. No: Name: 16-2. (40 points) Begin by graphing the cube root function, y=√x. Then use the basic transformations in 1.6 to graph y=-2 √(x-2)+1. Sketch each step when one transformation is applied and write down the corresponding algebraic expression.

Please print your full name in capital letters.
No: Name: 16-2. (40 points) Begin by graphing the cube root function, y=√x. Then use the basic transformations in 1.6 to graph y=-2 √(x-2)+1. Sketch each step when one transformation is applied and write down the corresponding algebraic expression.

Transcript text: Please print your full name in capital letters. No: $\qquad$ Name: $\qquad$ 16-2. (40 points) Begin by graphing the cube root function, $y=\sqrt{x}$. Then use the basic transformations in 1.6 to graph $y=-2 \sqrt{x-2}+1$. Sketch each step when one transformation is applied and write down the corresponding algebraic expression.

Solution

Solution Steps

Step 1: Graph the cube root function

The given function is $ y = \sqrt[3]{x} $.

Step 2: Apply the first transformation

The first transformation is a horizontal shift to the right by 2 units. The new function is $ y = \sqrt[3]{x-2} $.

Step 3: Apply the second transformation

The second transformation is a vertical stretch by a factor of -2 and a vertical shift up by 1 unit. The final function is $ y = -2\sqrt[3]{x-2} + 1 $.

Final Answer

The final transformed function is $ y = -2\sqrt[3]{x-2} + 1 $.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = x(1/3)", "y = (x-2)(1/3)", "y = -2*(x-2)**(1/3) + 1"], "latex_expressions": ["$y = \\sqrt[3]{x}$", "$y = \\sqrt[3]{x-2}$", "$y = -2\\sqrt[3]{x-2} + 1$"]}

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