Question

is f(x)=x+abs(x) continuous on [-2,1]

Answer 1

1. Are g(x) = x and h(x) = abs(x) continuous on [-2,1]?
2. Is the sum of two functions continuous on a given interval continuous on that interval?

Answer 2

I'm supposed to be using the Mean Value Theorem.

Answer 3

You can use the MVT once you know this function is continuous, but you shouldn't try to use the MVP to show that it is continuous.

Answer 4

i'm trying to figure out if it is continuous

Answer 5

So look at the two steps just wrote down for you.

1. Are g(x) = x and h(x) = abs(x) continuous on [-2,1]?
2. Is the sum of two functions continuous on a given interval continuous on that interval?

Answer 6

If the answers are yes and yes, you have your answer.

Answer 7

And they are.

Answer 8

on the graph of it it never even reaches -2

Answer 9

it is continuous but not differentiable