Question

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

Answer 1

Answer:

- Stretching the parent function $f(x) =\frac{1}{x}$  vertically .

 - Shifting the parent function $f(x) =\frac{1}{x}$  5 units right.

Step-by-step explanation:

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  $f(x) = \frac{100}{x -5}$ represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function $f(x) =\frac{1}{x}$ transformed to create the graph of $f(x) = \frac{100}{x -5}$?"

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 $0$   the function is compressed vertically by a factor of "b".

The exercise gives the following parent function:

$f(x) =\frac{1}{x}$

And you know that the transformed function which represents the remaining time in minutes needed to fill the tank, is:

$f(x) = \frac{100}{x -5}$

Therefore, based on the transformations explained before you can identify that the graph of the transformed function is created by:

- Stretching the parent function $f(x) =\frac{1}{x}$  vertically.

- Shifting the parent function $f(x) =\frac{1}{x}$  5 units right.

Answer 2

Answer:

C.) it is a vertical stretch with a factor of 100 and a translation 5 units down

Step-by-step explanation: