Identify a region given its restraint

Question

I am in a calc 3 class and we are currently working on absolute minimums and maximums of extremas of functions of two variables. First I will post an image of a HW question that I am having a bit of trouble with:

I am just not sure how to draw the graph for the region given the information D={(x,y) | 0 <= y <= x <= 4} How should I look at the constraints given for this region to be able to draw out its graph? Thank you!

Answer 1

The region $D$ is the intersection of three regions:

• $0 \le y$ is the upper half plane (everything above and including the $x$-axis)
• $y \le x$ is the region below and including the line $y = x$
• $x \le 4$ is everything to the left of and including the vertical line $x = 4$