### Graphs of Functions based on Rules

Of course, we can always make a graph from a function rule by substituting values in for the variable and getting the corresponding output value.

#### Graphing a Function based on Rules

1. Graph the following function:

Make a table of values. Pick a variety of negative and positive values for

-4 | |

-3 | |

-2 | |

-1 | |

0 | |

1 | |

2 | |

3 | |

4 | |

5 | |

6 | |

7 | |

8 |

It is wise to work with a lot of values when you begin graphing. As you learn about different types of functions, you will start to only need a few points in the table of values to create an accurate graph.

2. Graph the following function:

Make a table of values. We know

0 | |

1 | |

2 | |

3 | |

4 | |

5 | |

6 | |

7 | |

8 | |

9 |

Note that the range is all positive real numbers.

#### Real-World Application

The post office charges 41 cents to send a letter that is one ounce or less and an extra 17 cents for each additional ounce or fraction of an ounce. This rate applies to letters up to 3.5 ounces.

Make a table of values. We can’t use negative numbers for

### Example

#### Example 1

Graph the following function:

Make a table of values. Even though

-2 | |

-1 | |

0 | |

1 | |

2 |

Note that the range is all positive real numbers, and that this looks like an absolute value function.

### Review

Graph the following functions.

- Vanson spends $20 a month on his cat.
- Brandon is a member of a movie club. He pays a $50 annual membership and $8 per movie.
f(x)=(x−2)2 f(x)=3.2x f(t)=27t−t2 f(w)=w4+5 f(x)=t+2t2+3t3 f(x)=(x−1)(x+3) f(x)=x3+x25 f(x)=2x−−√

### Review (Answers)

To view the Review answers, open this PDF file and look for section 1.13.