Graphing Question: x<1, 1≤x≤2, x>2

[you_of_eh]

The function is..

f(x) = 2x-2 if x<1
x^2 if 1 <= x <= 2
7-x if x>2

I made a table of values and graphed the points. The problem is my prof said something about not all of the points being connected by straight lines, some being connected by curves. I was wondering why this is, and for which points?

 

[LCKurtz]

What does the graph of f(x) = x² look like?

 

[you_of_eh]

It's a parabola.

..so would the line between the two points of the function f(x) = x^2 be curved and all others straight?