Graphing Question: x<1, 1≤x≤2, x>2

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SUMMARY

The discussion centers on the piecewise function defined as f(x) = 2x - 2 for x < 1, f(x) = x^2 for 1 ≤ x ≤ 2, and f(x) = 7 - x for x > 2. The graph of f(x) includes both linear and quadratic segments, leading to curves between certain points. Specifically, the segment defined by f(x) = x^2 is a parabola, which inherently creates a curved line between the points at x = 1 and x = 2. The other segments, being linear, connect their respective points with straight lines.

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