Question 102559
{{{y=7+sqrt(3x+21)}}} Start with the given expression


Remember you cannot take the square root of a negative value. So that means the argument {{{3x+21}}} must be greater than or equal to zero (i.e. the argument <font size=4><b>must</b></font> be positive)


{{{3x+21>=0}}} Set the inner expression greater than or equal to zero


{{{3x>=0-21}}}Subtract 21 from both sides



{{{3x>=-21}}} Combine like terms on the right side



{{{x>=(-21)/(3)}}} Divide both sides by 3 to isolate x 




{{{x>=-7}}} Divide



So that means x must be greater than or equal to -7



So here is the domain in interval notation: [-7,*[Tex \LARGE \infty])



Notice if we graph {{{y=7+sqrt(3x+21)}}} , we get

{{{ graph( 500, 500, -10, 10, -2, 18, 7+sqrt(3x+21)) }}} notice how the graph never crosses the line {{{x=-7}}}. So this graphically verifies our answer.


and we can see that x must be greater than or equal to -7 in order to lie on the graph