The function f(x) is defined such that f(x) = x + 2 , if x <= 1 and f(x) = x^2, if x > 1.

At the point x = 1, if we approach from the left

lim x--> 1- [ f(x)] = 1 + 2 = 3.

If we approach from the right,

lim x--> 1+ [f(x)] = 1^2 = 1

The value of lim x--> 1- [ f(x)] is not equal to lim x--> 1+ [f(x)].

**Therefore the function is discontinuous.**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now