1. ## Translations Question

Hi, in our math class we're reviewing content from previous years, and I've run into a problem! This is the question:

The function r(x) = $\displaystyle \frac{1}{x+3}$ is transformed by a translation of 3 units up and 5 units to the right. The transformed function passes through the point (x,7). The value of x to the nearest hundredth is __.

The answer I'm getting for x is 6:

$\displaystyle r(x) = \frac{1}{x+3}$
$\displaystyle y = \frac{1}{(x-5)}+6$
$\displaystyle 7 = \frac{1}{(x-5)}+6$
$\displaystyle 1 = \frac{1}{(x-5)}$
$\displaystyle 1(x-5) = 1$
$\displaystyle x-5 = 1$
$\displaystyle x = 6$

Am I overlooking something? The answer in the back of the book says 2.25, however I know the back of the book has been wrong in the past so I'd like to see if it's my mistake or the back of the books mistake. Thanks in advance!

2. Originally Posted by cb220
Hi, in our math class we're reviewing content from previous years, and I've run into a problem! This is the question:

The function r(x) = $\displaystyle \frac{1}{x+3}$ is transformed by a translation of 3 units up and 5 units to the right. The transformed function passes through the point (x,7). The value of x to the nearest hundredth is __.

The answer I'm getting for x is 6:

$\displaystyle r(x) = \frac{1}{x+3}$
$\displaystyle y = \frac{1}{(x-5) {\color{red}+ 3}}+{\color{red}3}$ Mr F says: Note the corrections in red. Do you understand why ......? r(x) --> r(x - 5) + 3 ....

[snip]
Now simplify, substitute y = 7 and solve for x.

3. Ah I see, so I can't group together the +3 within the denominator with the vertical translation of +3. Trying this has produced 2.25, the correct answer Thanks!