How do you find the domain of #f(x) = 8 /( x + 4)#?

2 Answers
Jul 13, 2017

Answer:

Domain: #(-oo,-4)uu(-4,oo)#

Explanation:

The domain of a rational function is all the values except for those which that make it undefined. In other words, the denominator of a rational function cannot be #0#.

To find which values exactly make the rational function undefined, we set the denominator not equal to #0# and solve for #x#

#x+4!=0#

#x+cancel(4-4)!=0-4#

#x!=-4#

What we have solved for tells us the values (#x-#values to be precise) that cannot be in the domain.

Therefore our domain is all real numbers except #-4#. In interval notation, this is:

#(-oo,-4)uu(-4,oo)#

What this tells us about the graph as well is that there is a vertical asymptote defined by the line #x=-4# (See graph)

graph{8/(x+4) [-23.37, 16.63, -9.44, 10.56]}

Jul 13, 2017

Answer:

Domain of #f(x) = (-oo, -4)uu (-4, +oo)#

Explanation:

#f(x) = 8/(x+4)#

#f(x)# is defined for all x except #x=-4# where the function is undefined.

#:.# the domain of #f(x) = forall x in RR: x!= -4#

In interval notation: Domain of #f(x) = (-oo, -4)uu (-4, +oo)#

The domain can be seen on the graph of #f(x)# below.

graph{8/(x+4) [-32.47, 32.48, -16.24, 16.23]}