Function f of x = the absolute value of expression x + 3 is graphed. The x-axis goes from negative 6 to 6. The graph is a V-shaped line. The line starts at (negative 6, 3), moves downward to (negative 3, 0), moves upward and ends at (6, 9). The region between the line and the x-axis, between x = negative 5 and x = 5, is shaded. The shaded region is divided into 10 rectangles of width 1. Each rectangle touches the line at the top left corner.
The following graph shows a Riemann sum:
Function f of x = start fraction 1 over x end fraction + 2 is graphed. The x-axis goes from negative 1 to 8. The graph consists of 2 curves. The first curve starts in quadrant 2 and moves downward toward the y-axis in quadrant 3. The second curve starts in quadrant 1 and moves downward toward about y = 2. The region between the curve and the x-axis, between x = 2 and x = 7, is shaded. The shaded region is divided into 10 rectangles of width 0.5. Each rectangle touches the curve at the top right corner.
