Question

Question #62ad6

Answer 1

Range `= (-oo, 0) U (0, +oo)`

graph{1/(x+1) [-9.43, 10.57, -5.52, 4.48]}

Explanation:

We need to find the Range of the function `y = f(x) = 1/(x + 1)`

First, we need to figure out where our "Asymptotes" are:

Set the "Denominator" equal to zero.

Therefore `(x + 1) = 0`

Hence, `x = (-1)`

At `x = -1`, our function `f(x) = 1 / (x + 1)` is "undefined"

Our "Vertical Asymptote" is `x = -1`

To find whether we have a "Horizontal Asymptote", check the highest degree of the Numerator (NR) and Denominator (DR) of our rational function.

In the NR, there is no `x-term` and hence, the higher degree of NR is equal to zero.

In the DR, the highest degree is equal to 1.

If the degree of the DR is larger than the degree of the NR then `y = 0` is the Horizontal Asymptote.

Refer to the graph to observe the behavior of the rational function `y = f(x) = 1/(x + 1)`.