Respuesta :
- Stretching the parent function f(x) = 1/x vertically .
- Shifting the parent function f(x) = 1/x 5 units right.
The complete exercise is: " A 100 gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The function f(x) = 100/(x-5) represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function f(x) = 1/x transformed to create the graph of f(x) = 100/(x-5) ?"
Below are some transformations for a function :
1. If f(x) +k, the function is shifted "k" units up.
2. If f(x) -k, the function is shifted "k" units down.
3. If f(x) -k , the function is shifted "k" units right.
4. If f(x) +k , the function is shifted "k" units left.
5. If bf(x) and b>1 the function is stretched vertically by a factor of "b".
6. If bf(x) and 0<b<1 the function is compressed vertically by a factor of "b".
The exercise gives the following parent function:
f(x) = 1/x
And you know that the transformed function which represents the remaining time in minutes needed to fill the tank, is:
f(x) = 100/(x-5)
Therefore, based on the transformations explained before you can identify that the graph of the transformed function is created by:
- Stretching the parent function f(x) = 1/x vertically.
- Shifting the parent function f(x) = 1/x 5 units right.
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