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Cogito

Algebra 2 · Chapter 1 · Lesson 2

Practice Worksheet

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

NameDate

Figure — use these to answer the problems

Move the V around and watch its corner follow.

y = 1|x + 0| + 0

Stretch a1

Shift0

Lift0

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

y = |x − 7| + 3. What is the minimum value?
Answer
y = |x + 2|. What is the x of the vertex?
Answer
y = |x| + 7. What is the minimum value?
Answer
y = −|x|. Is the vertex a maximum? 1 for yes, 0 for no.
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

y = |x − 4|. What is y at x = 1?
Answer
f(x) = 2x for x < 3, else 10. What is f(1)?
Answer
Same function. What is f(8)?
Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

8
Match each change to its effect on the V.
Draw a line from each item on the left to its match on the right.
- |x − h|
- |x| + k
- −|x|
- Moves right by h
- Lifts by k
- Flips it upside down
y = |x|. How many x values give y = 4?
Answer
The Corner
y = |x − 5|. What is the x of the vertex?
Answer
The Value
y = |x − 5| + 1. What is y at x = 5?
Answer