Answer
$$
f(x)=\frac{x^{2}+6 x+9}{|x|+3}
$$
is continuous for all real numbers $x$ in domain $f $
Work Step by Step
$$
f(x)=\frac{x^{2}+6 x+9}{|x|+3}
$$
The function being graphed is a rational function, and hence is continuous at every number where the denominator is nonzero.
But the equation
$$
|x|+3=0
$$
has no solution because $ |x|+3 \gt 0 $ for all $x$ in the domain
Therefore the function
$$
f(x)=\frac{x^{2}+6 x+9}{|x|+3}
$$
is continuous for all real numbers $x$ in domain $f $
