How do you find the domain and range of $f(x) = - ( 1 / ( x + 1) )$ ?

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Answer 1 · 2017-12-03T12:08:00

Domain: $" " x < -1 or x > -1$

Range: $" " f(x) < 0 or f(x) > 0$

Using interval notations

Domain: $" "(-oo, -1) uu (-1, oo)$

Range: $" "(-oo, 0) uu (0, oo)$

We are given the function $f(x) = -(1/(x+1))$

To find the Domain of $f(x)$ , set $color(green)(x+1 = 0)$

$rArr (x + 1) = 0$

$rArr x = -1$

We must remember that $x = -1$ is our Vertical Asymptote

So, our Domain is $(-oo, -1) uu (-1, oo)$

To find the Range of $f(x)$

Let us now observe our original function $f(x) = -(1/(x+1))$

We note that there is no x term in the numerator(NR)

Hence, the degree of numerator is ZERO(0).

The highest degree of the denominator(DR) is ONE(1).

We observe that degree of the DR $>$ degree of the NR

Hence, we conclude that $y=0$ is our Horizontal Asymptote

Range: $" " f(x) < 0 or f(x) > 0$

Range using interval notations is $(-oo, 0) uu (0, oo)$

Please investigate the graph for a visual comprehension

enter image source here

How do you find the domain and range of f(x) = - ( 1 / ( x + 1) ) f(x) = - ( 1 / ( x + 1) ) ?