Question

What are the holes, VA, domain, HA, and Range of n+8/6n? Please help!!

Answer 1

Holes: None

Domain:

`n \\e0`

HA:

`y = (1)/(6)`

Range:

`y\\e (1)/(6)`

Explanation:

The given rational expresion is

`(n + 8)/(6n)`

The expresion has no common factor in both the numerator and the denominator hence there is no hole.

The domain refers to all values of n, for which the expression is defined.

The domain is all real numbers except

`n = 0`

The horizontal asymptote is the horizontal line the expression approaches as n goes to infinity.

Since both numerator and denominator have the same degree, the horizontal asymptote is the ratio of the leading coefficients.

`y = (1)/(6)`

The range refers to all y-values for which n is defined.

Let

`y = (n + 8)/(6n)`

We solve for n, to get:

`6yn = n + 8`

`6yn - n = 8`

`n(6y - 1) = 8`

`n = (8)/(6y - 1)`

The range is all y-values except

`6y - 1 = 0 \\ y = (1)/(6)`