Absolute value functions and equations
Solve the equation over ℝ. If it has only one solution, leave the second box empty.
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The absolute value of a number is its distance from zero: |3| = 3 and |−3| = 3. The graph of y = |x| looks like the letter V with its vertex at (0, 0). The graph of y = |x − 2| + 1 is the same V, just shifted 2 to the right and 1 up.
What does this generator do?
At the easy level it draws a V-shaped graph and you choose the formula. At the medium level you solve equations like |x − 3| = 5. At the hard level there is a number in front of x, for example |2x + 4| = 6. Sometimes the equation has one solution or none.
How to use it
1) For a graph, find the vertex (a, b) and write y = |x − a| + b. Careful: a vertex to the right of the y-axis means a minus inside the bars. 2) Split the equation |expression| = c into two: expression = c or expression = −c. 3) If c is negative, the equation has no solution. If c = 0, it has one.