find the domain of x+7/x.x-8x+4
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Answer:
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
+
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:
(
−
∞
,
−
4
)
∪
(
−
4
,
∞
)
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]}
Step-by-step explanation:
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