Algebra HW Help

Question

Graph the function by using transformations of the graph of y=1/x. Plot all necessary asymptotes. For vertical asymptotes, make sure there are at least two points on each side.

F(x)=1/x-3

Answer 1

for F(x) = (1/x) -3, the graph is a rectangular hyperbola of 1/x shifted vertically down by 3. It is two branches, with a vertical asymptote x=0 and horizontal asymptote y=-3

two points on the graph include (1, -2) and (-1, -4)

but if the problem is F() = 1/(x-3) then the graph is also a rectangular hyperbola with a horizontal rightward shift of 1/x by 3

this hyperbola also has 2 branches, with a vertical asymptote of y=3 and a horizontal asymptote of y=0

two points on the graph include (1, -1/2) and (5, 1/2)

the way the problem is written F(x) = 1/x-3 is slightly ambiguous, but technically it means (1/x)-3, although odds are good the intended problem was meant to be 1/(x-3)