M5.1.2 For the adult
The modulus function
How far is a number from zero, when I do not care which way I walk?
What this chapter teaches
The modulus |x| is the distance of x from 0, so it is never negative. |x − a| is the distance from x to a, so |x − 2| < 5 means x is within 5 of 2: −3 < x < 7. The graph of y = |f(x)| keeps the part of y = f(x) above the x axis and folds the rest up. When an equation has x on both sides, every answer must be checked.
Three questions to ask
There is no one right wording. Listen for the idea.
- What numbers are within 5 steps of 2 on the number line?
- Why can |x − 3| never equal −4?
- How does the graph of y = |2x − 3| differ from the graph of y = 2x − 3?
After the chapter, the learner can
- Sketch y = |2x − 3|
- Solve |x − 2| < 5
What they copy into their notebook
|x| is the distance from 0. |x − a| < b means a − b < x < a + b. y = |f(x)| folds the part below the x axis upwards. Check every answer to |…| = an expression in x.