Determine the domain and the range of the
Domain and range are concepts that many students have trouble with, so you are not alone!
Domain is the x values of the relation.
Range is the y values of the relation.
If you have trouble remembering which one is which , like I do, D comes before R, just like x comes before y;)
To determine if a relation is a function, there are several tests that you can use. For every x value, there can be one and only one y value. If there is more than one y value for any x value, it is not a function.
Another test is the vertical line test. If a vertical line only goes through one point on the line, it is a function. If it goes through two points on the line, it is not a function.
As an example, let's look at y = (x-3)^2 + 6.
This parabola is in the form, y=a(x-h)^2 + k, where a indicates a stretch or compression, and whether the parabola opens up or down. If a is positive, it opens up, and the y value of the vertex represents a minimum. If a is negative, it opens down, and the y value of the vertex is a maximum. The values h and k are the x and y values of the vertex.
In this case, a is one, so the parabola opens up, with a minimum value of 6.''
Now back to the domain and range.
Since we can use any value for x in the equation, for the domain, x is an element of real numbers, sometimes written (xER).
For the range, y can only be greater than or equal to the minimum. So the range is y is an element of all real numbers, such that y is greater or equal to 6, sometimes written (yER'y>=6). Sorry I couldn't find the greater than or equal to character;)
Good luck.
Paul
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