Answer:
Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.
Step-by-step explanation:
We are asked to describe the transformation of function [tex]y=\frac{3}{4x-12}[/tex] as compared to the graph of [tex]y=\frac{1}{x}[/tex].
We can write our transformed function as:
[tex]y=\frac{3}{4(x-3)}[/tex]
[tex]y=\frac{3}{4}*\frac{1}{(x-3)}[/tex]
Now let us compare our transformed function with parent function.
Let us see rules of transformation.
[tex]f(x-a)\rightarrow\text{Graph shifted to the right by a units}[/tex],
[tex]f(x+a)\rightarrow\text{Graph shifted to the left by a units}[/tex],
Scaling of a function: [tex]a*f(x)[/tex]
If a>1 , so function is stretched vertically.
If 0<a<1 , so function is compressed vertically.
As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.
As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.
Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.
