Answer:
- Stretching the parent function [tex]f(x) =\frac{1}{x}[/tex] vertically .
- Shifting the parent function [tex]f(x) =\frac{1}{x}[/tex] 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 [tex]f(x) = \frac{100}{x -5}[/tex] represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function [tex]f(x) =\frac{1}{x}[/tex] transformed to create the graph of [tex]f(x) = \frac{100}{x -5}[/tex]?"
Below are some transformations for a function :
1. If [tex]f(x)+k[/tex], the function is shifted "k" units up.
2. If [tex]f(x)-k[/tex], the function is shifted "k" units down.
3. If [tex]f(x)-k[/tex], the function is shifted "k" units right.
4. If [tex]f(x)+k[/tex], the function is shifted "k" units left.
5. If [tex]bf(x)[/tex] and [tex]b>1[/tex] the function is stretched vertically by a factor of "b".
6. If [tex]bf(x)[/tex] and [tex]0<b<1[/tex] the function is compressed vertically by a factor of "b".
The exercise gives the following parent function:
[tex]f(x) =\frac{1}{x}[/tex]
And you know that the transformed function which represents the remaining time in minutes needed to fill the tank, is:
[tex]f(x) = \frac{100}{x -5}[/tex]
Therefore, based on the transformations explained before you can identify that the graph of the transformed function is created by:
- Stretching the parent function [tex]f(x) =\frac{1}{x}[/tex] vertically.
- Shifting the parent function [tex]f(x) =\frac{1}{x}[/tex] 5 units right.
