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

2 Answers
Anthony R.
Jul 13, 2017

Domain: (-oo,-4)uu(-4,oo)(−∞,−4)∪(−4,∞)

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 00.

To find which values exactly make the rational function undefined, we set the denominator not equal to 00 and solve for xx

x+4!=0x+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]}

Alan N.
Jul 13, 2017

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]}

Related questions
See all questions in Domain and Range of a Function
Impact of this question
6278 views around the world
You can reuse this answer
Creative Commons License