Question

Is the function given by, (Picture Provided)

Answer 1

Answer:

a. yes

Step-by-step explanation:

The given function is

$f(x)=\left \{ {{3x-2,if\:x\le3} \atop {10-x,if\:x\:>\:3}} \right.$

$f(3)=\left \{ {{3(3)-2,if\:x\le3} \atop {10-3,if\:x\:>\:3}} \right.=7$

$\lim_{x \to 3^-} f(x)=3(3)-2=7$

$\lim_{x \to 3^+} f(x)=10-3=7$

$\Rightarrow \lim_{x \to 3} f(x)=7$

Since;

$\lim_{x \to 3} f(x)=f(3)$

The function is continuous at $x=3$