Answer
Not continuous
Work Step by Step
We are given the function:
$f(x)=\dfrac{2x^2+3x+1}{x^2+5x}$
We use the continuity checklist to determine if $f$ is continuous in $a=-5$:
1) $f(x)=\dfrac{2x^2+3x+1}{x^2+5x}=\dfrac{2x^2+2x+x+1}{x(x+5)}$
$=\dfrac{2x(x+1)+(x+1)}{x(x+5)}=\dfrac{(x+1)(2x+1)}{x(x+5)}$
$a=-5$ is a zero of the denominator, therefore $f$ is not defined for $a=5$.
As the condition 1 from the continuity checklist is not satisfied, the function is not continuous in $a=-5$.
