Cogito
Algebra 2 · Chapter 1 · Lesson 2
Piecewise and Absolute Value Functions
A V-shape is two lines in disguise.
11 problems · about 22 minutes · F-IF.C.7, F-BF.B.3
What this lesson teaches
The student graphs and evaluates absolute value and piecewise functions.
- y = |x| is a V with its corner at the origin.
- The same transformation rules move and flip it as any other function.
- A piecewise function needs the right condition chosen before anything is computed.
Warm Up
Straightforward practice. Get the method working first.
4 problemsy = |x − 7| + 3. What is the minimum value?
Answer 3
Why 3.
y = |x + 2|. What is the x of the vertex?
Answer -2
Why (x + 2) is (x − (−2)).
y = |x| + 7. What is the minimum value?
Answer 7
Why Zero plus 7.
y = −|x|. Is the vertex a maximum? 1 for yes, 0 for no.
Answer 1
Why It opens downward.
Build It Up
The same ideas with more to keep track of.
3 problemsy = |x − 4|. What is y at x = 1?
Answer 3
Why |−3|.
f(x) = 2x for x < 3, else 10. What is f(1)?
Answer 2
Why 1 is below 3.
Same function. What is f(8)?
Answer 10
Why 8 is not below 3.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each change to its effect on the V.
Answer |x − h| → Moves right by h; |x| + k → Lifts by k; −|x| → Flips it upside down
Why Inside is horizontal, outside is vertical.
y = |x|. How many x values give y = 4?
Answer 2
Why Both arms of the V.
The Corner: y = |x − 5|. What is the x of the vertex?
Answer 5
Why 5.
The Value: y = |x − 5| + 1. What is y at x = 5?
Answer 1
Why 1.