Question

How do you determine the value a line is continuous on?

Answer 1

What's the actual question you're working on?

Answer 2

Determine the value of c such that the function is continuous on the entire real line.
X+3 \[x \le2\]
cx+6 x>2

Answer 3

the x is less than or equal to 2 is supposed to be next to the (X+3)

Answer 4

I know. It's a piecewise function.

Answer 5

You find the value of c by setting x = 2, then setting
x + 3 = cx + 6
2 + 3 = 2c + 6
5 = 2c + 6
0 = 2c + 6 - 5
0 = 2c + 1
-1 = 2c
-1/2 = c

So the function is continuous on the entire real line when c = -1/2

Answer 6

ohh okay. thank you again!