Question

Using y=1/x as the parent function, make your own transformations (5 units right, reflect on x axis, 2 units down, horizontal compression with factor 2). Then graph and state domain and range.

Answer 1

First, we have a translation of 5 units right. That means the value of x is decreased by 5 units (x' = x - 5)

So we have:

`y=(1)/(x-5)`

Then, we have a reflection over the x-axis, which means the value of the function changes signal (y' = -y)

`y=-(1)/(x-5)`

Finally, we have a translation of 2 units down, which means the value of the function is decreased by 2 units (y' = y - 2)

`y=-(1)/(x-5)-2`

Adding a horizontal compression by a factor of 2 means the value of x will be multiplied by 2 (x' = 2x)

`y=-(1)/(2x-5)-2`

Graphing this function, we have:

The domain is all values x can assume. Since we have a fraction, its denominator can't be zero, so:

`\begin{gathered} 2x-5\\e0 \\ 2x\\e5 \\ x\\e2.5 \end{gathered}`

So the domain is:

`(-\propto,2.5)\cup(2.5,\propto)`

The range is all values y can assume. Since the fraction can't have a value of zero, we have:

`\begin{gathered} y\\e0-2 \\ y\\e-2 \end{gathered}`

So the range is:

`(-\propto,-2)\cup(-2,\propto)`