Question

Follow the "Four-Step method of graphing a piecewise defined function" to graph the f(x). [Refer to the canvas notes for these steps] Label the coordinates of the end points of each piece and indicate if the point is to be included or excluded from the curve by drawing either a solid circle [if point is included in the graph] and an open circle [if the point is not included in the graph] about the end point.

f(x)=( x², if x<2
x, if x⩾2
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Answer 1

To graph the function f(x), follow the Four-Step method of graphing a piecewise defined function. Plot the points for each piece and connect them to form the curve. Label the end points and indicate if they are included or excluded on the graph.

Step-by-step explanation:

To graph the function f(x), we can use the Four-Step method of graphing a piecewise defined function. The function f(x) is given as follows:

f(x) = x², if x < 2
f(x) = x, if x ≥ 2

1. Step 1: Determine the end points of each piece. The end point of the first piece is x = 2, and the end point of the second piece does not exist since it continues indefinitely.
2. Step 2: Determine if the end point is included or excluded in the graph. The end point x = 2 is included in the graph, so we draw a solid circle around it.
3. Step 3: Plot the graph for each piece. For the first piece, x < 2, we plot the points (x, x²) for x values less than 2. For the second piece, x ≥ 2, we plot the points (x, x) for x values greater than or equal to 2.
4. Step 4: Connect the points to form the curve for each piece. The graph should consist of a parabola for x < 2 and a straight line for x ≥ 2.

Remember to label the coordinates of the end points and indicate if the point is included or excluded from the curve. Use a solid circle for included points and an open circle for excluded points.