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

1 Answer
Dec 3, 2017

Answer:

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)#

Explanation:

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

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