# Functions from tables and graphs

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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:

What is then say f (5)? We read it of from the graph as:

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. Up a level : IB Mathematics
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Next page : Quadratic functions Last modified: Jan 8, 2017 @ 19:15