The
axes below show the relevant portions of the graphs of functions f
and g. Each is a piecewise linear function, which means that
the portions of the graphs that look like straight lines are indeed straight
lines. Fill in the table below when the requested values exist. ((gof)(x)
means g(f(x)).
| x | 1 | 3 | 5 | 7 |
| f(x) | 2 | 3 | 3 | 3 |
| f'(x) | 1 | 0 | 0 | 0 |
| g(x) | 2.5 | 1.5 | 0.5 | 1 |
| g'(x) | -0.5 | -0.5 | -0.5 | 1 |
| (f+g)(x) | ? | ? | ? | ? |
| (f+g)'(x) | ? | ? | ? | ? |
| (f-g)(x) | ? | ? | ? | ? |
| (f-g)'(x) | ? | ? | ? | ? |
| (fg)(x) | ? | ? | ? | ? |
| (fg)'(x) | ? | ? | ? | ? |
| (f/g)(x) | ? | ? | ? | ? |
| (f/g)'(x) | ? | ? | ? | ? |
| (g/f)(x) | ? | ? | ? | ? |
| (g/f)'(x) | ? | ? | ? | ? |
| (gof)(x) | ? | ? | ? | ? |
| (gof)'(x) | ? | ? | ? | ? |
| (fog)(x) | ? | ? | ? | ? |
| (fog)'(x) | ? | ? | ? | ? |