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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 graph a negative inside a square root. Besides keeping track of the domain, it will also be very important for you to graph very neatly, or you will probably get most of your graphs wrong. By the way, "graphing radicals" usually means "graphing square roots", so most of the examples below deal with square roots.
First off, I need to check the domain. I know that you can't graph a negative inside a square root, so, for instance, x cannot be 5, because:
To find the domain, I set whatever is inside the radical equal to or greater than zero, and solve: 3 – x
> 0
Now I know that I shouldn't pick an x-value that is greater than 3 for your 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. This is what many students typically do: They pick only two or three points, and they pick them very close together:
They plot these few points:
...and then they draw a straight line through them!
But I know better, so I pick more useful points:
...and I plot them very neatly:
...and then I draw a curved line through them, remembering not to extend the line to the right of x = 3:
You should expect radicals 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 does make graphing simpler. On the other hand, if you have a graphing calculator, you may be able to have the calculator compute all your T-chart values for you. Check your manual. Top | 1 | 2 | 3 | Return to Index Next >>
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Elizabeth Stapel 2006-2008 All Rights Reserved
