What Values of C Make the Function Continuous?

[Arshad_Physic]

Homework Statement

for what values of the constant c is the function f everywhere continous
f(x) cx+7 if x<= 2
(cx)^2 +1 if x>2

i don't understand how to do continuous functions so can someone please explain the
process?

 

[lanedance]

make the right & left hand limit at the point x = 2 equivalent

 

[HallsofIvy]

What is $\displaytype \lim_{x\to 2^_} f(x)$?
(That's the same as $\displaytype\lim_{x\to 2} cx+ 7$)

What is $\displaytype\lim_{x\to 2^+} f(x)$?
(That's the same as $\displaytype \lim_{x\to 2} (cx)^2+ 1$)

In order that f(x) be continuous at x= 2, those must be equal and both equal to f(2)= 2c+ 7.