Find all vertical, horizontal, and slant asymptotes of the graph of the function.

Question

Find all vertical, horizontal, and slant asymptotes of the graph of the function.

f(x) = x³/2x²-50

Answer 1

the function is rewritten as (x/2) + (25/2)( (1/2)/(x+5) + (1/2)/(x-5))

after dividing the polynomials and calculating the partial fraction decomposition.

the vertical asymptotes are at x=5 and x=-5

there is an oblique asymptote on the line y = x/2

Here is a table of values on the intervals (-infinity,-5) U ( -5 , 5) U ( 5, infinity)

x y

0 0

-1 1/48

1 -1/48

10 20/3

-10 -20/3

2 -4/21

-2 4/21

the graph is positive but decreasing on (-5,0),

negative and decreasing on (0,5)

the tail chains of the graph are in between the

vertical asymptotes and the oblique asymptote

Answer 2

x³/2x²-50 =x/2-50. None of what you were asked for exists as this is just a linear equation (a line)