Question

For each function below, find its domain and then determine if the function increasing, decreasing, or constant on each piece of the domain. Sometimes the domain is just one interval, but the function still changes its behavior at some points. s(t)=
`(-5)/(|t|)`

The interval on which the function is decreasing is : ( , )
The interval on which the function is increasing is : ( , )
The interval on which the function is constant is : ( , )
Leave unused fields blank.

Answer 1

Answer and explanation:

First, the domain is all real numbers except 0, since x = 0 is the asymptote.

D: x ∊ R, x ≠ 0

or

D: (-∞, 0) ∪ (0, ∞)

The range is everything below y = 0.

R: y < 0

or

R: (0, -∞)

Next, this function is never constant so there are only intervals of increasing and decreasing. The intervals meet at x = 0.

inc: x > 0

dec: x < 9

or

inc: (0, ∞)

dec: (0, -∞)