Question
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
Whe equation of a hyperbola is given by
Write down the equation of the new function that is formed when
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
Ask by Rodriguez Todd. in South Africa
Dec 28,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The transformed hyperbola equation is
with asymptotes at
and
.
Solution

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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!