1. ## Unable to understand this question about graph transformation

The question is probably very simple but I just can't seem to understand what it wants.

I've drawn out both of the graphs alongside their asymptotes is that all it wants? Am I overthinking this question?
It says to transform but I don't know how to transform between these two/ which one I transform from.

2. ## Re: Unable to understand this question about graph transformation

Well the problem asks you to use the graph of $\displaystyle y= \frac{1}{x}$ to graph this new function. I presume that you know that the graph of $\displaystyle y= \frac{1}{x+ 1}$ is just the graph of $\displaystyle y= \frac{1}{x}$ shifted to the left one unit. So how does multiplying that by x change the graph?

3. ## Re: Unable to understand this question about graph transformation

I would use the fact that

$$\dfrac{x}{x+1} = \dfrac{(x+1)-1}{x+1} = \dfrac{x+1}{x+1} - \dfrac{1}{x+1} = 1 - \dfrac{1}{x+1}$$

along with the hint HallsofIvy gave you.

4. ## Re: Unable to understand this question about graph transformation

So quickly drawing it out as 1/x and then 1/x+1 and finally x/x+1 I get the following -

I can say that it moves to the left once and then it gets reflected and moves up by 1 when numerator 1 is replaced with x?

Correct.