Question

Use four rectangles to approximate the area under the graph of f(x) = 2x+3 and above the x-axis from x = 0 to x = 4. Let the height of each rectangle be the function value on the
right side.

Answer 1

Can you sketch this quickly?

Answer 2

OK. Looks pretty good but not exactly right.

Answer 3

what is the y-intercept for this function?

Answer 4

I believe its 3 and 11

Answer 5

The y-intercept is where the function crosses the y-axis, the value for x = 0, and there f(x) = 3. OK. But otherwise this is fine and we can continue with it OK?

Answer 6

ok

Answer 7

Now, you've drawn four rectangles over the region from x= 0 to x =4. Re-read the problem description to figure out what you haven't done as they wanted.

Answer 8

I'm not sure was I suspost to find the area.

Answer 9

We'll get there. Notice that the rectangles touch the line on their left sides, and now that I look again, you haven't actually got a rectangle from x = 0 to x = 1. Do you see that?

Answer 10

yes

Answer 11

Why don't you redraw the figure with all those changes. y-intercept at 3, 4 rectangles touching on their right sides, not left. OK?