Question 162851
Determine the domain:
Recall that the domain of a function is the set of all of the values of the independent for which the function is defined, in other words, all of the x-coordinate values.
{{{f(x) = sqrt(x^2+8x)}}} Notice that, for some values of x, the radicand becomes negative and, at these points, the function is not defined, thus these values of x would be excluded values.
What values of x would make {{{(x^2+8x) < 0}}}
The answer might be easier to see if you were to factor the radicand:
{{{(x(x+8)) < 0}}}
If x = -7, you would have:
{{{(-7(-7+8)) = -7}}} So x = -7 is a candidate for eclusion.
if x = -6, you would have:
{{{(-6(-6+8)) = -12}}} So x = -6 is a candidate for exclusion.
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If x = -1, you would have:
{{{(-1(-1+8)) = -7}}} So x = -1 is a candidate for exclusion.
For all other values of x, the function is defined.
So the domain would be:
{{{-7 > x >= 0}}}