# Thread: Sketch the graph of a continuous function

1. ## Sketch the graph of a continuous function

Hi again I'm tackling a question that is very likely to be on a future exam, and I'm a bit stuck.

The question:

g(x){ 0 if x<2
2 if 2<x<4
-1 if x>4

Sketch the graph of a continuous function f(x) knowing that f(0)=1, and f'(x) = g(x)

Graphing g(x) is not a problem, but understanding how to formulate a seperate function with just the info given is a major roadblock.

2. Originally Posted by ughintegrals
Hi again I'm tackling a question that is very likely to be on a future exam, and I'm a bit stuck.

The question:

g(x){ 0 if x<2
2 if 2<x<4
-1 if x>4

Sketch the graph of a continuous function f(x) knowing that f(0)=1, and f'(x) = g(x)

Graphing g(x) is not a problem, but understanding how to formulate a seperate function with just the info given is a major roadblock.

If $\displaystyle g(x) = \left\{ \begin{array}{cl} 0 & \text{if}\; x < 2\\ 2 & \text{if}\; 2 < x < 4\\ -1 & \text{if}\; x > 4 \end{array}\right.$

then

$\displaystyle f(x) = \left\{ \begin{array}{cl} c_1 & \text{if}\; x \le 2\\ 2x + c_2 & \text{if}\; 2 < x \le 4\\ -x + c_3 & \text{if}\; x > 4 \end{array}\right.$.

Then use the fact that $\displaystyle f(0) = 1$ (this gives you $\displaystyle c_1$) and that $\displaystyle f(x)$ is continuous at $\displaystyle x = 2$ and $\displaystyle x = 4$ (this gives the remaining constants.)

3. ugh, im almost there.

c1 was no sweat, but how am i supposed to use the x= 2 and x = 4 to solve the remaining constants? plug 2 into the 2x+c, or equate it to 2? or neither?

im just a bit stuck there....sorry for being difficult.