Which graphs represent a function

Value tables and function graphs

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In these explanations you will learn the relationship between value tables and graphical representations of linear functions.

Tables of values

A function can be represented in different ways, one possibility is the value table.

From the table of values ​​to the graphic representation

The graph of a linear function is a straight line. A straight line is clearly defined by two points. You can find the coordinates of these points in the table of values ​​and enter them in a suitable coordinate system.
Given is the table of values ​​of a linear function f. Draw the graph of the function.
Enter points in the coordinate system

Tables of values ​​and graphical representation for material tasks

There are many situations in everyday life that you can describe with the help of linear functions. If you want to draw the graph (the straight line) for a factual situation with a linear connection, you first consider which coordinate system is suitable. The labeling and scaling of the coordinate axes and are important the choice of the quadrants of the coordinate system. In order to make the right decisions here, you are guided by the definition and value range of the function and what information you want to take from the graphical representation.
Ms. Meier is going away for a few days. To prevent her plants from drying out on the windowsill, she places a 10-liter bucket with water next to it and attaches a woolen thread to each flower pot, one end of which is in the water and the other end of which is in the ground.The water now runs evenly from the bucket into the flower pots. After half a day there are still 8 liters in the bucket and after 2.5 days there are still 4 liters. How much water did Ms. Meier put in the bucket? After what time is the bucket only half full? After how many days is the bucket empty ?
Enter points in the coordinate system and draw straight lines