Question

graph the function f(x)=((1)/(x-2))+2, think in terms of transformations (opr translation) of f(x)=(1/x). What is the vertical asymptote? What is the horizontal asymptote?

Answer 1

The vertical asymptote is 2 because you cannot divide by 0 and 2-2=0 would be the denominator. The horizontal asymptote is found when you take the limit as x=>inf and that would be 0, so the horiz. asymptote would be at x=0

Answer 2

for f(x) to be defined :
\[x \neq 2\]
hence X=2 will be vertical asymptote.
and horizontal asymptote will be X= \[\int\limits_{x}^{\infty} f(x)=0\]

Answer 3

for vertical asymptote:\[\large x-2=0\]\[\large x=2\]
for horizontal asymptote:
numerator degree is smaller than denominator degree then x-axis is the horizontal asymptote.

Answer 4

no sorry, the limit value will be 2 hence horizontal asymptotes will be X=2.

Answer 5

no
for horizontal asymptote y=0

Answer 6

when i graph it on the calculator, it looks like the horizontal and vertical asymptotes are 2. I can see where the asymptotes are on the calc, but i need to show all work. can you please show the steps?

Answer 7

another time sorry,
horizotal asymptotes will be Y=2.

Answer 8

When infinity is in place of x and is in the denominator, then the numerator values are trivial, thus it would be x=0

Answer 9

horizontal will be y=0
not y=2

Answer 10

may you show me the steps in how you got the answers?

Answer 11

\[\lim_{x \rightarrow \infty} 1/x = 0\] I used 1/x because it gives you the same result, but you are able to focus on the reason why it gives you 0 instead of focusing on the other numbers.

Answer 12

cosider it ,the function is \[f(x)=(1\div (x-2))+2\] not

Answer 13

when you put X=\[\infty\]..then you get f(x)=2

Answer 14

If infinity is in the denominator and you have constants everywhere plus and nothing is raised to a power, then it goes to 0.

Answer 15

I appreciate all the help, but without using a calculator, what are all the steps in finding the answer?

Answer 16

The vertical asymptote is found when the denominator is equal to zero, in this case it is 2.

The horizontal asymptote is found when you treat x as infinity, in this case if you do so you end up with 0.

Answer 17

may you write that in a math equation? I need to show all steps of the work.

Answer 18

x-2=0 x=2, sorry but I can't do all the work for you

Answer 19

There are two translations here. The subtraction inside the basic function moves the graph two units to the right. The two added at the end moves it two units up. That means the vertical and horizontal asymptotes move two right and two up from where they start