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We start by graphing f(x) = (1/2)x+3.
This is a line with y-intercept y(0)=3.
We calculate another point so we can draw the line that goes through both points.
For example, when x=-6, y=0.
So we have the points (0,3) and (-6,0) that belongs to the line.
We can use them to draw the line:
We can now draw g(x).
This function is defined in parts: one function for x<=0 and other for x>0.
When x<=0, the function is g(x)=4-x^2.
This is a quadratic function. When x=0, y=4, so we know the y-intercept.
When x=2, y=0, so we now know the x-intercept.
We can aproximate the function with these two points:
