determine the value c that f is continuous

Question

anonymous · Answer

$$f(x)=$$ $$x+3;x \le3$$
$$cx+6; x >2$$

anonymous · Answer

i think there is a mistake here

anonymous · Answer

is it maybe 
$$f(x) = \left\{\begin{array}{rcc}
x + 3 & \text{if}  & x \leq 3 \
cx+6& \text{if}  & x >3
\end{array}
\right.$$

anonymous · Answer

thats it. can you help?

anonymous · Answer

yea, put $x=3$ and set them equal

anonymous · Answer

you get 
$$3+ 3=c\times 3+6$$
$$6=3c+6$$
$$c=0$$

anonymous · Answer

your answer is 
$$f(x) = \left\{\begin{array}{rcc}
x + 3 & \text{if}  & x \leq 3 \
6& \text{if}  & x >3
\end{array}
\right.$$

anonymous · Answer

I have the answer as c=-1/2

anonymous · Answer

was it maybe this
$$f(x) = \left\{\begin{array}{rcc}
x + 3 & \text{if}  & x \leq 2 \
cx+6& \text{if}  & x >2
\end{array}
\right.$$

anonymous · Answer

because $c=-\frac{1}{2}$ is not right

anonymous · Answer

yes. sorry.

anonymous · Answer

then set 
$$2+3=c\times 2+6$$
$$5=2c+6$$
$$2c=-1$$
$$c=-\frac{1}{2}$$

anonymous · Answer

ok that makes sense. 

what about for maybe this
f(x)={x+1 if 1<x<3
          $$x ^{2} +bx+c$$   if $$\left| x-2 \right|$$>1

anonymous · Answer

the answer being b=-3, c=4