Summary
Highlights
The final example is f(x) = 1/x when x < 0, f(x) = 3 when 0 ≤ x < 3, and f(x) = -x + 5 when x ≥ 3. For x < 0, the left side of the reciprocal function 1/x is drawn. For the constant part, a horizontal line at y=3 is drawn from x=0 (closed circle) to x=3 (open circle). For x ≥ 3, the linear function -x+5 begins with a closed circle at (3,2) and continues downwards.
The tutorial begins by introducing the concept of graphing piecewise functions. The first example presented is f(x) = x when x < 0 and f(x) = 5 when x ≥ 0. The individual graphs of y = x and y = 5 are shown separately to understand their shapes.
The graph of y = x is used for x < 0, marked with an open circle at (0,0) (since x=0 is not included). The graph of y = 5 is used for x ≥ 0, marked with a closed circle at (0,5) (since x=0 is included). This combines the left side of y=x with the right side of y=5.
The second example is f(x) = 2 when x < 1 and f(x) = x + 3 when x > 2. For x < 1, a horizontal line at y=2 is drawn, with an open circle at (1,2) as 1 is not included. For x > 2, the line y = x + 3 is drawn, starting with an open circle at (2,5).
This example covers f(x) = 2x + 1 when x < 1, f(x) = 1 when x = 1, and f(x) = -x² when x > 1. For the linear part (2x+1), an open circle is placed at (1,3). For x=1, a single closed point is at (1,1). For the quadratic part (-x²), an open circle is placed at (1,-1) and the downward-opening parabola is drawn for x > 1.
The fourth example is f(x) = 3x + 4 when x < 0, f(x) = 2 when x = 0, and f(x) = √x when x > 1. For x < 0, a linear function 3x+4 with an open circle at (0,4) is drawn. For x = 0, a closed point is marked at (0,2). For x > 1, the square root function is drawn, starting with an open circle at (1,1).