Can a parallel to the x-axis be a graph of a function?

What you need:

• Basic terms coordinate system and functions

Parallel to the x-axis - the graph

• In a two-dimensional coordinate system (with x- and y-axis) countless graphs of images, relations and of course functions can be displayed.
• The parallels to the y- and x-axis represent two special features, which are noticeable simply because of their special graphs. In principle, these can easily be drawn as a graph - a simple set square is sufficient to construct the parallels at any distance from the two axes.

What are the functions behind it?

Easy to draw, but these parallels are, too Functions and what are their names?

• In the case of a function that appears as a graph in an xy coordinate system, each x value is uniquely (!) Assigned one (and only one) y value. For example, the function rule y = x is a function which, as a graph, is a straight line, namely the bisector in the 1st and 3. Quadrant of the axbox, has.
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• You can do a simple ruler test yourself: Simply run the graph of your function from left to right with a ruler or set square perpendicular to the x-axis. If there is a function, the ruler may only intersect the graph at one point. If there are two points of intersection, it is not a function.


Determine certain points in the graph arithmetically - this is how it works

A math problem: You have the graph of a function and ...

• If there is a parallel to the x-axis, assign exactly one y-value to each x-value; the ruler test is also successful here. It is irrelevant (and also allowed) that all x-values ​​lead to the same y-value, because it is a parallel. And: No single x-value is assigned two (or more) y-values. Parallels to the x-axis are therefore functions by definition.
• The functional equations of such parallels have the form y = b, where b is any value from the real ones Counting can be. For example, y = 3 represents a parallel to the x-axis that is at a distance of 3 from the x-axis.
• The situation is different if your graph is parallel to the y-axis. An example is x = 5, a parallel that goes through the x value "5". Here you assign 5 innumerable y-values ​​(in principle all real numbers) to the x-value. So it is not a function, as the ruler test shows.

By the way: You can also use Equations Find. The x-axis has the functional equation y = 0. You can write down the y-axis as x = 0, but it is not a function (see above).