Graphing a piecewise function with multiple functions

[Emworthington]

Homework Statement

Suppose f(x) is a piecewise function defined as follows

f(x) = 2x^2+2 ---- > x < 1
= 2x^2 - 3x ----- > 1 ≤ x ≤ 2
= 2 - (6/x) ----- > x > 2
Graph f(x) for 0 ≤ x ≤ 3Find the left and right hand limits of f(x) as x approaches 1 and as x approaches 2

Homework Equations

N/A

The Attempt at a Solution

I don't know how to go about graphing this piece wise graph. Can I plug in any number that satisfies the inequality and then graph the x and y values for each equation, and then connect the coordinates? That doesn't seem right, because I need the same x value for each function, but that doesn't seem possible for the inequalities. What numbers can I plug in?

 

[iRaid]

Just take each piece at a time..

For the first when, whenever x > 1, graph the graph 2x^2+2
Next, between 1 and 2, graph 2x^2-3x
And so on..