Question
The equation of a hyperbola is given by
.
Write down the equation of the new function that is lormed when
is transformed as follows:
Write down the equation of the new function that is lormed when
Ask by Savage Vega. in South Africa
Jan 03,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Here are the equations after each transformation:
-
Shift two units to the left:
-
Shift 3 units up:
-
Shift 1 unit right and 2 units down:
-
New hyperbola with asymptotes at
and :
Solution

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Bonus Knowledge
To find the equations for the transformed hyperbola under the given conditions, we start with the original function
.
-
Shift two units to the left: This means substituting
with . The new function becomes: -
Shift 3 units up: We add 3 to the entire function:
-
Shift 1 unit right and 2 units down: First, we shift right (substituting
with ), then we subtract 2: -
New asymptotes at
and : The general form of a hyperbola is . To shift the vertical asymptote to , we set :
Putting all transformations together, the final equation of the new hyperbola is: