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I am in need of a little algebra help. I have received this problem from an online site, and I figured out what values I need to plot on the number line:

enter image description here

In the range of this number line, I know I need to plot -1,2, and 7, as they are the answer to this equation (I am correct, right?). But, I am not exactly sure how to plot those points… One of the two dots means that value is included, the other means that that value is not included, but I am not sure right now. The icon of the line is the button that fills the space between two points with a line. Does anybody have any idea?\

BTW: I got my answers by going through all the numbers shown on the number line, and entering them for $x$, and the numbers are the values from the number line that return a real number when submitted into $x$

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The answer you want to plot is wrong -- but I can't figure out what you did wrong to get it. Could you explain how you got the numbers $-1$, $2$ and $7$? (It is true that $f$ is defined for those numbers, but they are far from the only numbers it is defined for). – Henning Makholm Feb 2 '12 at 17:11
Could you please tell us what is the full problem or the site address where the problem is? – NoChance Feb 2 '12 at 17:31
The site this is on I have to login to, so going to this site won't work. And I cannot make a link, either... – fr00ty_l00ps Feb 2 '12 at 18:06

1 Answer 1

up vote 2 down vote accepted

There is a better way to determine the domain than guess and check. You know that the value of the function has to be real - that's your starting point. For it to be real, 4x + 8 has to be greater than or equal to zero; that is, 4x + 8 >= 0. Solve that for x, and you will get an inequality that tells you what values of x are valid. You just have to communicate that on the number line. The solid dot means you include that point (greater than or equals), the open dot means you don't (greater than). I hope that's enough to get you started without ruining the learning experience for you.

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Remember, the function includes a square root... – fr00ty_l00ps Feb 2 '12 at 19:15
And anyways, do I just put the dot on the number that will return a real number? – fr00ty_l00ps Feb 2 '12 at 19:17
Exactly. If you take the square root of a negative number, you get an imaginary result. With that constraint, you know that 4x + 8 >= 0 in order for the result to be real. Without the square root, the domain would be all numbers. – redneckjedi Feb 2 '12 at 19:19
You're going to wind up with a whole range of numbers that give you real numbers. The dot goes on the boundary of the range, and filling it in or not tells you whether to include the boundary or not. – redneckjedi Feb 2 '12 at 19:20
So in this case I would fill in the line, correct? – fr00ty_l00ps Feb 2 '12 at 19:34

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