## sha0403 2 years ago 2x+4 if x<-1 X^2+1 if -1≤x<2 F(x) 3-x if 2<x<4 3 if x=4 7-2x if x>4 help me to find the value of x where the function f(x) is continuous.

1. empraptor

Does the question ask for values where f(x) is not continuous? I ask because there are an infinite number of values for x at which f(x) is continuous.

2. sha0403

no..it just ask where the function is continuous...

3. empraptor

Maybe they are limiting the question to the 3 values (1,2 and 4) that are at the boundaries of the subdomains. In that case, what you could do is draw a graph of the function and see at which of these three points the graph is continous.

4. sha0403

how to draw the graph? can u explain to me?

5. empraptor

(Correction: the subdomain boundaries are -1, 2 and 4.) Draw the line y=2x+4 to the left of x=-1. Draw the parabola \[y=x^2+1\] for x between -1 and 2. Draw the line y=3-x for x between 2 and 4. Draw a point at y=3 for x=4. Draw line y=7-2x to the right of x=4.

6. sha0403

ok can u explain me the feature of continuous graph?

7. empraptor

A function that's continuous at a particular point usually looks "connected" at that point when its graph is drawn.

8. sha0403

ok i will try..btw thank u for help me.. =)

9. empraptor

Keep in mind that even if two pieces of the function look like they come together at some value of x, the function is not be continuous if just one point is not connected there.