The parent function is:
[tex]$y=\frac{1}{x}[/tex]
The transformed function is:
[tex]$y=\frac{1}{2 x-10}-3[/tex]
[tex]$y=\frac{1}{2(x-5)}-3[/tex]
[tex]$y=\frac{1}{2}\left(\frac{1}{x-5}\right)-3[/tex]
Comparison of simplified transformed function with the parent function:
- The function multiplying by a number indicates dilation.
- The function is being compressed in vertical direction by a factor of 2 if the number lies between 0 and 1.
- Subtracting a number from x indicates a horizontal shift towards right.
- That is the parent function is transformed 5 units to right.
- Subtracting a number from the function indicates a downward shift.
- That is the parent function is transformed 3 units down.
Hence the graph of [tex]y=\frac{1}{2 x-10}-3[/tex] is the graph of [tex]y=\frac{1}{x}[/tex] stretched vertically, shifted right by 10 unit and shifted 3 unit down.
The image of the graph is attached below.
