Question

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

Answer 1

The parent function is:

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

The transformed function is:

$\frac{1}{2x-10}-3 \\ \\ = \frac{1}{2(x-5)}-3 \\ \\ = \frac{1}{2}( \frac{1}{x-5} ) -3$

If we compare the above simplified function with the parent function we can note the following transformations:

1) Multiplication by 1/2
Multiplying the function by a number indicates dilation. Since the number is between 0 and 1, the function is being compressed in vertical direction by a factor of 2. 

2) Subtraction of 5 from x.
Subtracting a number from x indicates a horizontal shift towards right. This means the parent function is transformed 5 units to right.

3) Subtraction of 3 from the function.
Subtracting a number from the function indicates a downward shift. This means the parent function is transformed 3 units down.

The above 3 transformations are done on y = 1/x to get the new function.