Graphing Absolute Value Functions on a Coordinate Plane
Absolute value means 'number away from zero' so the absolute value of -1 = 1.
#1: On the graph of Y = |X|, it is symmetric in the y-axis because for every point (x, y) on the graph, the point (-x, -y) is also on the graph and it makes a V shape. The Y-intercept = 0 and the 1 in front of the X means go up one right one. Since the X could also be -X you need to go up one left one as well. When the extended lines are drawn you can see the V-shape this function creates.
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#2: Solve | 2x – 3 | – 4 = 3. First, isolate the absolute-value part; that is, I'll get the absolute-value expression by itself on one side of the "equals" sign, with everything else on the other side | 2x – 3 | = 7 Now I'll clear the absolute-value by splitting the equation into two, one for each sign:
(2x – 3) = 7 or –(2x – 3) = 7 2x = 10 or –2x = 4 x = 5 or x = –2 So the solution is x = –2, 5. |