Question

State the horizontal asymptote of the rational function.
\(\large f(x)=\dfrac{x^2+4x-7}{x-7}\)

Answer 1

@phi

Answer 2

(x-\(\sqrt11\))(x+\(\sqrt11\))

Answer 3

I just plotted it, and it does not have a horizontal asymptote. But we can do this.
Divide x-7 into the top.
we get
\[ x + 11 + \frac{70}{x-7} \]

if the last part is tiny (compared to the first part), then it's a bit like
y = 1x + 11
which is the equation of a line that it approaches.
in other words, the asymptote is that equation

Answer 4

So would it be none?
These are my choices
None
y = -4
y = 7
y = 6

Answer 5

Here is the plot.

Answer 6

Are you sure you don't have a typo in the equation ?

Answer 7

http://prntscr.com/4s1thf

Answer 8

oh, it would be it has none

Answer 9

The fast way is to look at the "degree" of the top and bottom
They degree has to be the same to get a horizontal asymptote

in your problem, the degree of the top (i.e. the biggest exponent) is 2
the degree of the bottom is 1
different degrees means *no horizontal asymptote*

Answer 10

can you help me with a few more? i can open them as a different question

Answer 11

ok