Question

The function f is defined by f(x)= x^2-2x+3 if x≤1 and f(x)=-2x+5 if x > 1

Is f continuous at x=1? How do I solve this

Answer 1

let's find f(1) for both functions
if f(x) = x^2-2x+3 , then f(1) = 1 - 2 + 3 = 2
if f(x) = -2x + 5 , then f(1) = -2 + 5 = 3

so clearly there is a "jump" at x = 1
let's look at the graph
http://www.wolframalpha.com/input/?i=plot+f(x)%3D+x%5E2-2x%2B3+,+f(x)%3D-2x%2B5

delete the part of the parabola which is greater than 1
delete the part of the straight line, which is less than 1

can you see the final result, and the gap from 2 to 3 in the y value?

Answer 2

Thank you. How would I be able to tell if this is continuous without using a graph though?