Step 1
Graph
[tex]\begin{gathered} y=\frac{1}{x} \\ \end{gathered}[/tex]We use values of x= -3 o 3
[tex]\begin{gathered} x=-3 \\ y=-\frac{1}{3} \\ x=-2 \\ y=-\frac{1}{2} \\ x=0 \\ y=undefined \\ x=1 \\ y=\frac{1}{1}=1 \\ x=3 \\ y=\frac{1}{3} \end{gathered}[/tex]We will now plot the graph of
[tex]y=\frac{5}{x+6}[/tex]using the points of x=-10,-9,-8,-3,-2,-1,1
[tex]\begin{gathered} x=-3 \\ y=\frac{5}{-3+6} \\ y=\frac{5}{3} \\ x=-2 \\ y=\frac{5}{4} \\ x=-1 \\ y=\frac{5}{5}=1 \\ x=0 \\ y=\text{ undefined} \\ x=1 \\ y=\frac{5}{7} \\ x=2 \\ y=\frac{5}{8} \\ x=\frac{5}{9} \end{gathered}[/tex]Together, they will look like this;
Hence, a possible solution is;
[tex]y=\frac{2}{3},\:x=\frac{3}{2},\:\quad \:x\ne \:0,\:x\ne \:-6[/tex]The graphs compare thus;
From the first and second graphs, we can see that they intersect at a point (1.5, 0.667).
Both graphs have the same shape but the following differences:
By looking at the graph we can see that the graph of y=5(x+6) is translated six units to the left with respect to the graph of y=1/x.
