Question

How do the graphs of y = 1/x and y=5/x+6 compare?

Answer 1

Answer:

$y=\frac{5}{x+6}$ stretches out the graph by 5 times and makes the graph 6 units higher as compare with $y=\frac{1}{x}$

Step-by-step explanation:

Given two functions $y=\frac{1}{x}$ and $y=\frac{5}{x+6}$

We have to compare the two graphs.  

Here, the graph of $y=\frac{1}{(x+6)}$ is obtained by  a translation shift to left by 6 from the graph of $y=\frac{1}{x}$.

and also the graph of $y=\frac{5}{x+6}$ is  obtained by a stretching 5 upwards from the graph $y=\frac{1}{x+6}$

Hence,  $y=\frac{5}{x}$ stretches out the graph by 5 times. It increases and decreases 5 times more.  

$y=\frac{5}{x+6}$ stretches out the graph by 5 times and makes the graph 6 units higher as compare with $y=\frac{1}{x}$