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Graphing Radical Functions: Introduction (page 1 of 3)

Graphing radical equations is probably the first time you've had to consider the domain of the equation before you graph. This is because you cannot put a negative value inside a square root. In addition to keeping track of the domain, you will also need to graph very neatly, or you could easily get most of your graphs at least partially wrong. Since "graphing radical functions" usually means "graphing functions involving square roots", most of the examples below deal with square roots.

  • Graph y = sqrt(3 - x)   Copyright Elizabeth Stapel 2000-2011 All Rights Reserved

    First off, I need to check the domain of this function, so I know where not to try to plot points. I know that I can't graph a negative inside a square root, so, for instance, x cannot be 5, because:

      sqrt(3 - 5) = sqrt(-2)

    To find the domain of this function, I set whatever is inside the radical (the "argument" of the radical) to be equal to or greater than zero, and then I solve:

      3 x > 0
      3 > x

      x < 3


    Now I know that I shouldn't pick any x-value that is greater than 3 for my table of values (often called a "T-chart"). And I also should not try to draw anything on my graph to the right of x = 3: if I can't have any x-values past 3, then I can't very well have the graphed line go past 3.

    The following is what many students typically do: They pick only two or three x-values, and they pick them very close together:


    They then plot only these few points:

plotted points

    ...and then they draw a straight line through them!


    But I know better, so I pick not only more x-values, but also useful x-values which will give me nice "neat" values for plotting:


    Then I plot these values very neatly:

plotted points

    ...and then I draw a curved line through them, remembering not to extend the line to the right of x = 3:

y = sqrt(3 - x)

You should expect radical functions to graph as curved lines. Do not try to put a straight line through these points. You should also expect radical graphs to be much wider than they are tall. Be sure to use adequate space on your paper for a good graph.

I was careful to pick x-values for my T-chart that gave nice neat y-values. This is not required, nor is this even always possible. But it can make graphing much simpler.

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Cite this article as:

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


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