Question

Describe the graph of y=1/2x-10 -3 comapred to the graph of y= 1/x

Answer 1

The parent function is:

$y=\frac{1}{x}$

The transformed function is:

$y=\frac{1}{2 x-10}-3$

$y=\frac{1}{2(x-5)}-3$

$y=\frac{1}{2}\left(\frac{1}{x-5}\right)-3$

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 $y=\frac{1}{2 x-10}-3$ is the graph of $y=\frac{1}{x}$ stretched vertically, shifted right by 10 unit and shifted 3 unit down.

The image of the graph is attached below.