Previous page : Functions, Quiz 2, composite functions

Next page : Quadratic functions

**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.

Previous page : Functions, Quiz 2, composite functions

Next page : Quadratic functionsLast modified: