Modulus Functions and Modulus Equations
Read the modulus as distance from zero, sketch the V-shaped graph it produces, and solve equations and inequalities that contain one.
What a learner can do afterwards
- Sketch y equals the modulus of a linear expression and mark where the graph turns
- Solve a modulus equation by splitting into the two cases and rejecting solutions that fail the original
- Solve a modulus inequality and write the answer as an interval or a union of intervals
1 · Read
Read the bars as stretch from zero. The graph makes a V whose bend sits where the inner line hits zero. For y shaped by x minus 3, the bend lands at (3, 0).
Split each equation into twin cases, one per sign. For bars round 2x minus 4 set to 6, work 2x minus 4 as 6 and as minus 6. The roots are 5 and minus 1.
Each root must face the first equation. Some guests fail at the door, as in bars round x set to x plus 2, where 1 breaks the check and just minus 1 stays. Keep just the ones that pass.
Gaps use stretch sense too. Bars round x minus 1 under 4 means within 4 of 1, so minus 3 through 5. Past marks split outward with OR: bars round x minus 2 past 5 means x past 7 or x under minus 3.
Split by sign, test each guest in the first equation, and read gaps as near or far.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.