# Problem of the Week Problem E Everything in its Place 3

1. A Venn diagram has two circles, labelled A and B.

Each circle contains functions, $$f(x)$$, that satisfy the following criteria.

• A: $$f(2)=-3$$

• B: $$f(-2)=-1$$

The overlapping region in the middle contains functions that are in both A and B, and the region outside both circles contains functions that are neither in A nor B.

In total this Venn diagram has four regions. Place functions in as many of the regions as you can. Is it possible to find a function for each region?

2. A Venn diagram has three circles, labelled A, B, and C.

Each circle contains ordered pairs, $$(x,y)$$, where $$x$$ and $$y$$ are real numbers, that satisfy the following criteria.

• A: $$y=(x+3)^3+2$$

• B: $$y=\dfrac{1}{2}x^2+1$$

• C: $$y=|x+1|$$

In total this Venn diagram has eight regions. Place ordered pairs in as many of the regions as you can. Is it possible to find an ordered pair for each region?