Cogito
Algebra 1 · Chapter 3 · Lesson 5
Piecewise Functions
Different rules on different stretches.
11 problems · about 22 minutes · F-IF.C.7
What this lesson teaches
The student evaluates a piecewise function and interprets it in context.
- A piecewise function applies a different rule on each stretch of inputs.
- Decide which condition holds before computing anything.
- The conditions must not overlap, or it would not be a function at all.
Warm Up
Straightforward practice. Get the method working first.
4 problemsf(x) = 5x for x < 2, else x + 50. What is f(1)?
Answer 5
Why 5.
f(x) = 2x for x < 5, else 100. What is f(3)?
Answer 6
Why 3 is below 5.
Same function. What is f(9)?
Answer 100
Why 9 is not below 5.
Same function. What is f(5)?
Answer 100
Why The first piece needs strictly below 5.
Build It Up
The same ideas with more to keep track of.
3 problemsMay two pieces both claim the same input? 1 for yes, 0 for no.
Answer 0
Why That would give two outputs.
f(x) = x + 1 for x ≤ 0, else 4x. What is f(0)?
Answer 1
Why 0 satisfies x ≤ 0.
Same function. What is f(2)?
Answer 8
Why 4 × 2.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsOrder the steps for evaluating a piecewise function.
Answer 1. Check which condition the input satisfies 2. Select that rule only 3. Substitute into it
Why Choosing comes before computing.
Is a postage cost by weight band piecewise? 1 for yes, 0 for no.
Answer 1
Why The rule changes at each band.
Below the Threshold: f(x) = 3x for x < 4, else x + 20. What is f(2)?
Answer 6
Why 6.
Above It: Same function. What is f(10)?
Answer 30
Why 30.