The graph of the piecewise function features three line segments with slopes 2, 1/2, and -1, each corresponding to specific intervals of x.
The provided function is f(x) = 2x + 4 for x ≤ -2, f(x) = 4 + 1/2x for -2 < x < 2, and f(x) = -x + 5 for x ≥ 2. To graph this function, we'll analyze each part separately.
For x ≤ -2: The function is a linear equation, f(x) = 2x + 4, representing a line with a slope of 2 and a y-intercept of 4.
For -2 < x < 2: The function is f(x) = 4 + 1/2x, indicating a line with a slope of 1/2 and a y-intercept of 4.
For x ≥ 2: The function is f(x) = -x + 5, representing a line with a slope of -1 and a y-intercept of 5.
Plotting these segments on a graph, we will have three lines, each corresponding to a different range of x-values. The first line has a slope of 2, the second has a slope of 1/2, and the third has a slope of -1.
In summary, the graph of the given piecewise function consists of three line segments with distinct slopes and intercepts based on the specified intervals.