Question

Suppose f is an increasing function and that f assigns the following values:

f(9) = 9, f(10) = 10, f(7) = 5, f(3) = – 4, f(5) = 3 and f(4) = – 1.

Answer 1

A value between 3 and 5 (exclusive of both) will do.

Example: You could choose 4 as a possible value.

Explanation:

`f(9)=9` means you have the ordered pair (9,9) on your graph.

`f(10)=10` means you have the ordered pair (10,10) on your graph.

`f(7)=5` means you have the ordered pair (7,5) on your graph.

`f(3)=-4` means you have the ordered pair (3,-4) on your graph.

`f(5)=3` means you have the ordered pair (5,3) on your graph.

`f(4)=-1` means you have the ordered pair (4,-1) on your graph.

Since f is increasing f(6) can be any value between 3 and 5, exclusive.

So you can assign any value for
`f(6)` such that
`3<f(6)<5`. We cannot conclude with out further information what value between 3 and 5, exclusive.