Answer
Not continuous
Work Step by Step
We are given the function:
$f(x)=\dfrac{5x-2}{x^2-9x+20}$
We use the continuity checklist to determine if $f$ is continuous in $a=4$:
1) Rewrite $f(x)$:
$f(x)=\dfrac{5x-2}{x^2-4x-5x+20}=\dfrac{5x-2}{x(x-4)-5(x-4)}$
$=\dfrac{5x-2}{(x-4)(x-5)}$
$a=4$ is a zero of the denominator, therefore $f$ is not defined for $a=4$.
As the condition 1 is not satisfied, the function is not continuous in $a=4$.
