# Thread: Applying dilations and reflection help

1. ## Applying dilations and reflection help

The function f is obtained from the graph of $\displaystyle y=\frac{1}{x}$ by the following transformations applied in the order given.
- a dilation by a factor of $\displaystyle \frac{1}{2}$ from the y-axis
- a reflection in the y-axis
- a translation of 3 units parallel to the x-axis (?)
- a translation of 1 unit parallel to the y-axis (?)

Write down the rule for f

Is this right for the first 2 transformations?

$\displaystyle y=-\frac{1}{2x}$

2. Originally Posted by user_5
The function f is obtained from the graph of $\displaystyle y=\frac{1}{x}$ by the following transformations applied in the order given.
- a dilation by a factor of $\displaystyle \frac{1}{2}$ from the y-axis
- a reflection in the y-axis
- a translation of 3 units parallel to the x-axis (?)
- a translation of 1 unit parallel to the y-axis (?)

Write down the rule for f

Is this right for the first 2 transformations?

$\displaystyle y=-\frac{1}{2x}$
Yes. f(x) --> f(2x) --> f(-2x).