Domain and range of a function

Mathematically speaking, relations refer to the set of ordered pairs, where the x values are the domain and the y values are the range. Now if that relation will show that the x values will only have one y element associated with it, then it becomes a function. So, if we’re given a set of ordered pairs (1,0) (2,5), (3,15), and (4,20) then we know that this illustrates a function. But if we’re given (1,0), (1,5) (2,15) (3,20) then we would know that this isn’t a function.

A function is written through the function notation f(x), say for example f(x) = 2x +5. F(x) simple means that for a particular value of x, the equation will be equal to a certain value. So if x is -1, then the function above will be f(-1) = 2(-1) + 3 which would give you the y value 3, thus your ordered pair would be (-1,1).

If we plot the values this function in a grid paper, we can easily verify whether this it really is a function or if its only a relation by applying the vertical line test. The vertical line test would be basically drawing a vertical line in the graph to see whether there is more than one point that the vertical line would intersect with. In graphing function we would also learn about the x intercept, where the y is equal to zero, and the y intercept where the x is equal to zero.

This chapter will have five parts that would discuss the basics things that we need to know about relations and functions. Understanding the basic concepts of the relations and functions is very important for the next chapters. There are several exercises that would illustrate what we have discussed earlier and would help us understand each concept covered by the chapter.

Domain and range of a function

The domain of a function is all the possible values of x’s of ordered pairs; whereas the range of a function is all the possible values of y’s of ordered pairs. You can easily find them by graphing the functions or ordered pairs. Let’s see how in this lesson.


  • 2.
    State the domain, range, and whether each is a function
  • 3.
    State the domain and range of each relation. Then determine whether each is a function.
    • b)

    • d)

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Domain and range of a function

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