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Graphing Radical Functions: Examples (page 2 of 3)

  • Graph y = -sqrt(3x - 2)

    First I'll find the domain by finding where the argument is non-negative:


     x >= 2/3

    Then I'll find some plot points:


    (How did I come up with the x-values that gave me such "nice" y-values? I started with the end values, and worked backwards. For instance, since 25 is a square, then 3x 2 = 25 gives me 3x = 27, or x = 9, as my starting value.)






    I'll plot the six points from my T-chart (above), and then I'll sketch my graph:


     y = -sqrt(3x - 2)

  • Graph y = 2sqrt(4x + 1) + 3
  • First I'll find the domain by finding where the argument is non-negative:

      x >= -1/4


    Next, I'll find some plot points at least five for my graph.



    I found my "neat" plot-points by setting the argument equal to a perfect square, such as 4 or 9, and then solving for x. Other x-values will work just as well; the choice is up to you.
      Copyright Elizabeth Stapel 2000-2011 All Rights Reserved



    Now I'll do my graph:



    Note that, since the graph "starts" at x = 1/4, the line should not go below or to the left of the "beginning" of the line. But the function continues forever in the other direction, so my graph needes to "continue" to the end of my drawing on the top right-hand "side" of the picture.


    y = 2sqrt(4x + 1) + 3

  • Graph y = sqrt(x^2 + 1)

    I'll first find the domain: I have to solve the quadratic inside the square root; it may be easier just to look at
    the graph of the quadratic.


    In this case, x2 + 1 is always above the x-axis (that is, it is always positive), so x can be anything; there is no restriction on the domain of this particular square-root function.


     y = x^2 + 1


    Next, I'll find some plot points:


    In this case, setting the argument, x2 + 1, equal to a perfect square and trying to solve did not work out usefully. Either the input values or the output values were going to be messy for this function. So I just used a calculator to find the approximate y-values, accurate to three decimal places, for my plot-points. This is more than sufficient for graphing.



     T- chart



    Finally, I'll do the graph:


    y = sqrt(x^2 + 1)

Note that, unlike an absolute value graph, this graph does not have an "elbow" at the bottom; it is curved. Don't go too quickly when graphing; take the time to notice details like this.

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Cite this article as:

Stapel, Elizabeth. "Graphing Radical Functions: Examples." Purplemath. Available from Accessed


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