What are the vertical and horizontal asymptotes for the function f (x) = StartFraction x squared + x minus 6 Over x cubed minus 1 EndFraction?

Given:

The given function is

We need to determine the horizontal and vertical asymptote.

Horizontal asymptote:

From the given function, it is obvious that the denominator's degree is greater than the numerator's degree.

Then, the horizontal asymptote is the x - axis.

Thus, the horizontal asymptote is

Vertical asymptote:

The vertical asymptote of the rational function are the undefined points and can be determined by equating the denominator equal to zero.

Thus, we have;

Solving, we get;

Thus, the function is undefined at the point

Hence, the vertical asymptote of the function is

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: