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Question 200239: my question states graph the piecewise function f(x)= 2-x if x greater than or equal to 0 and x^2=x>0. I know you can't show me the graph can you tell me how to do this? My textbook doesn't explain this well at all.
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! I think your problem statement is incorrect. As stated, both of the functions given are defined for x>0. If that is the case, then the functions are not piecewise.
One or the other must be defined when x is 'less than zero'.
Let's assume the first one is  for x<=0.
Plot this line for enough values of x to allow you to draw it. Since this is a line, you only need 2 points. Pick x=0 and x=-1 (note that both value chosen for x are <=0).
When x=0, f(x) = 2-0 = 2. So one point is (0,2)
When x = -1, f(x) = 2 - (-1) = 3, So another point is (-1,3).
Plot those two points and draw the ray (not the entire line) that starts at (0,2) and goes up to the left through (-1,3).
Now do the next 'piece' of the plot.
 x>0
This is a parabola, so you will need to plot a few more points in order to approximate the drawring.
Pick values if x > 0, so let's use x=1, x=2. We will also want to see what happens when x is 'very close to zero' (we will fudge and use 0).
When x=0 , x^2 = 0. So point is (0,0)
When x = 1, x^2 = 1. Another point is (1,1)
When x=2, x^2 = 4. Another point is (2,4)
Maybe one more point , x=3 will help
When x=3, x^2=9. So (3,9)
Now plot those points and draw the curve (U shaped) that connects them. Only draw in the curve for values of x>0.
Now you have both 'pieces drawn. You can see that each value of x has one and only one value for y. The plot 'jumps' at x=0. So the plot is not smooth.
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