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Algebra for Value Equations

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Given the equation: y = |2x - 1| + 1
Absolute value equations involving linear powers of x result in two lines which cross each other.
1. What are the equations of the two lines from the absolute value equation?
y1 = m1x1 + b1 and y2 = m2x2 + b2
2. Plot these two lines on a piece of graph paper.
3. What are the coordinates of the crossing point?
4. There are 4 half-lines which project out from the crossing point. Clearly mark which of the two half-lines constitute the answer to the absolute value equation. (Make the half-lines thicker and darker.)
5. What are the x-intercepts of your answer? (Write "none" if there are no x-intercepts.)
6. What are the y-intercepts of your answer? (Write "none" if there are no y-intercepts.)
7. What is the domain of x when y is increasing? (use interval notation)
8. What is the range of y when y is increasing?
9. What is the domain of x when y is decreasing?
10. What is the range of y when y is decreasing?
11. Let the absolute value equation be changed to
y < |2x - 1| +1.
Then shade in the area of the answer on your graph.

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Solution Summary

The expert determines the equations of the two lines from the absolute value equation.

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