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QUESTION 3
Whe equation of a hyperbola is given by .
Write down the equation of the new function that is formed when is transformed as follow
Shift two units to the left
Shift 3 units up
Shift 1 unit right and 2 units down
The equation of the new hyperbola has new asymptotes at and

Ask by Rodriguez Todd. in South Africa
Dec 28,2024

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The transformed hyperbola equation is with asymptotes at and .

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Beyond the Answer

To transform the equation , you will follow the sequence of shifts. First, shifting two units to the left modifies the function to , leading to . Next, shifting three units up gives , resulting in . Then, shifting one unit right and two units down modifies the function to , yielding .
Now, aligning with the new asymptotes and , we can conclude that the equation of the new hyperbola is:
.
So, the transformed function matches the desired asymptotes!

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