AFDA – Unit 3: Absolute Value and Piecewise Functions Name: _________________
Day 8 Notes: Review
Block: _____ Date:_______
Directions: Solve.
1. |3𝑥 + 7| = 4
2. −9|4𝑝 + 2| − 8 = −35
3. 2|𝑥 − 5| + 4 = 2
Directions: Solve, graph on the given number line, and write in interval notation.
2
4. −2|2𝑥 + 1| − 3 > 9
5. |𝑥 + 5| + 6 ≥ 27
6. − | − 𝑡 + 6| ≥ −14
3
Interval Notation:
Interval Notation:
Interval Notation:
_________________
_________________
_________________
Directions: Define the variable, write an inequality statement, and solve.
7. If a bag of chips is within 0.4 oz of 6 oz then it is allowed to go to market. What
range of weights is acceptable for the bags of chips to go to market?
8. The average height of a NYC Rockette is 68 inches. The dancers’ heights can vary
at most by 2 inches. What is the range of heights acceptable for the NYC Rockette
Dancers?
9.
Graph the function. Identify the vertex, axis of symmetry, and translations in
the space provided.
𝑦 = 2|𝑥 − 4| + 3
Vertex: ________
AoS: _________
Translations from parent graph:
10.
Graph the function. Identify the vertex, axis of symmetry, and translations in
the space provided.
3
𝑦 = − |𝑥 + 2|
4
Vertex: ________
AoS: _________
Translations from parent graph:
11.
Graph the function. Identify the vertex, axis of symmetry, and translations in
the space provided.
𝑦 = |𝑥 + 2| − 5
Vertex: ________
AoS: _________
Translations from parent graph:
Directions: Determine the equation of the given function and describe the translations.
12. 𝑎 =
Translations:
ℎ=
𝑘=
Equation:
13. 𝑎 =
Translations:
ℎ=
𝑘=
Equation:
14. 𝑎 =
ℎ=
𝑘=
Equation:
Translations:
15.
Identify the vertex, axis of symmetry, and graph the function.
𝑓(𝑥) <
2
| 𝑥 − 2| + 3
3
Vertex: ________
16.
AOS: _________
Identify the vertex, axis of symmetry, and graph the function.
𝑓(𝑥) ≥ |𝑥 + 5| − 2
Vertex: ________
17.
AOS: _________
Identify the vertex, axis of symmetry, and graph the function.
𝑓(𝑥) ≤ −3|𝑥 − 3| + 3
Vertex: ________
AOS: _________
18. Determine the inequality of the graphed function.
Test for Shading
𝑎=
ℎ=
𝑘=
Inequality: ___________________
19. Determine the inequality of the graphed function.
Test for Shading
𝑎=
ℎ=
𝑘=
Inequality: ___________________
20. Determine the inequality of the graphed function.
Test for Shading
𝑎=
ℎ=
𝑘=
Inequality: ___________________
Directions: Evaluate the piecewise function AND graph.
21.
−𝑥 + 3,
𝑓(𝑥) = { 1
− 𝑥 − 2,
3
𝑥<0
𝑥≥0
𝑓(−5)
𝑓(0)
𝑓(3)
−𝑥 + 2,
22.
1
𝑓(𝑥) = { 𝑥 + 1,
2
𝑓(−2)
𝑓(4)
𝑓(6)
𝑥≤2
2<𝑥<6
2,
𝑥≥6
23.
Write a piece-wise function that correspond with the following graph.
𝑓(𝑥) =
24.
_________________________,
______________
{_________________________,
______________
Write a piece-wise function that correspond with the following graph.
_________________________,
______________
_________________________,
______________
{_________________________,
______________
𝑓(𝑥) =
25. You have a summer job that pays “time and a half” for overtime (if you work more
than 40 hours). You make $9.50/hour.
a. Write a piecewise function that gives your weekly pay, P, in terms of the
number of hours you work, h.
b. How much will you make if you work 60 hours?