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Functions from tables
Let us look at the table we had in the beginning
| x | y |
| 1 | 1 |
| 2 | 4 |
| 3 | 7 |
| 4 | 3 |
| 5 | 2 |
| 6 | 1 |
Let us define f (x)=y using that table. That means that f (2)=4 and f (3)=7, and that the question “For what values of x is f (x)=1?” should be answered with 1 and 6.
So what is f (f (4)) given the table above? We have that f (4)=3 and f (3)=7, so the answer is 8.
Functions from graphs
Say the function g(x) is defined by the following graph:
Let us look at some possible questions.
What is then say f (5)? We read it of from the graph as:
We can read of the answer 1.5.
What is f (0.5)? We get 1.
At what x-value does is the maximum value of the function? We get x=3. At that point we have f(3)=4.
What is f(7)? It is undefined (a non filled circle).
What is the domain of the function? We have 0.5≤x<7.
What is the range of the function? We have 0.5<y≤4.
What is f (f (2.5))? We have f (2.5)=2, and f (2)=1.75. So the answer is 1.75.
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