Question

find the equations of both the horizontal and vertical asymptotes of the rational function. Show your work.
1. f(x)=(5x-1)/(x^2+9)
2. f(x)=(〖2x〗^2+8)/(x-1)

Answer 1

problem 1:
There are no real roots of the denominator therefore there are no vertical asymptotes; sicne the degre of the denominator exceed the degree o fthe numerator the horizontal asymptote is y=0 (the x-axis).

Answer 2

problem 2 is that the greatest integer function?

Answer 3

problem 2
there is a vertical asymptote located at x=1 since that is a real root of the denominator when the function is is lowest terms

Answer 4

says answer must be given as an equation of a line
sorry i am so lost here

Answer 5

problem 1
vertical asymptote: none (no equation can be given)
horizontal asymptote: y=0 (this is an equation for a line)

Answer 6

problem 2:
vertical asymptote: x=1 this is the equation for a vertical line)

Answer 7

problem 2
horizontal asymptote: none (no equation can be given)

Answer 8

problem 2 see attached graph; the dashed line is the VA x=1

Answer 9

problem1: see attached graph; notice how the graph approaches the x-axis as x goes to plus or minus infinity; the HA is y=0 (the x-axis)