Interval Notation for the Number LineDate: 03/04/2009 at 20:02:08 From: Lavern Subject: what does the graph of the interval [-4,10] look like What does the graph of the interval [-4,10] look like? I have no clue. All of Algebra is confusing. Date: 03/04/2009 at 23:12:10 From: Doctor Peterson Subject: Re: what does the graph of the interval [-4,10] look like Hi, Lavern. Interval notation is a way to identify a segment of a number line very compactly, by essentially boiling the graph itself down to its essentials. Take this interval as an example: o===========================* <--+---+---+---+---+---+---+---+---+---+---+---+---+--> -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Here I'm using "o" to represent an open dot that shows that a number at the end is NOT included in the set, and "*" for a closed (solid) dot that shows the end point IS included in the set. As an inequality this can be written as -3 < x <= 4 (-3 is less than x, and x is less than or equal to 4) Another way to draw the graph is to use a rounded parenthesis, "(" or ")" at a non-included endpoint, and a square bracket, "[" or "]", at an included endpoint: (===========================] <--+---+---+---+---+---+---+---+---+---+---+---+---+--> -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Interval notation is just a collapsed version of this form of graph. We first write the end indicator on the left, "("; then the value on the number line at that point, "-3", then, after a comma, the value on the right, "4", followed by the end indicator on the right, "]": (-3, 4] Thus this brief symbol says All numbers between -3 and 4, not including -3 but including 4. Your example has square brackets at both ends, so both -4 and 10 are included in the interval; so you'll draw a line from -4 to 10 and use the end indicators (solid dots or brackets) that you have been taught to use in that case. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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