Question

State the horizontal asymptote of the rational function.
f(x) = quantity five x plus one divided by quantity nine x minus two.

Answer 1

Just to be clear, the problem is this
\[\Large f(x) = \frac{5x+1}{9x-2}\]
right?

Answer 2

Yes

Answer 3

@jim_thompson5910 sorry, not sure why my page would not load

Answer 4

that's ok

Answer 5

The degree of the numerator and the denominator are the same. They are both 1. Do you agree with this statement?

Answer 6

Yes, I do

Answer 7

since the degrees are the same, this means we just divide the leading coefficients which are 5 and 9 in this case, so 5/9

Answer 8

the horizontal asymptote is simply the horizontal line y = 5/9

it's a horizontal line that cuts through 5/9 on the y axis

Answer 9

5/9 = 0.5556 approximately

Answer 10

Thank you so much!

Answer 11

no problem