new grade 10

1. MATHEMATICS
Absolute Value Functions
U Kyaw Swar Ohnn
Grade 10
Chapter 6
Kaung Htet Kyaw Private School

2. Two Dimensional Transformations

3. Six Types of Transformations
• Reflection
• Rotation
• Translation
• Enlargement
• Stretch
• Shear

4. • Reflection
object
image

5. • Rotation
object
image
𝜃

6. • Translation
object
image

7. • Enlargement
object image

8. • Stretch
object image

9. • Shear
object image

10. Chapter 6
Absolute value functions
• 6.1 Graph of the function 𝑦 = 𝑥 − ℎ + 𝑘
• 6.2 Graph of the function 𝑦 = − 𝑥 − ℎ + 𝑘
• 6.3 Graph of the function 𝑦 = 𝑎 𝑥
• 6.4 Graph of the function 𝑦 = 𝑎 𝑥 − ℎ + 𝑘
• 6.6 Inequality Involving 𝑥 − 𝑝
• 6.5 Equation 𝑥 − 𝑝 = 𝑞

11. Graph of 𝑦 = 𝑥

12. 𝑥 =
𝑥, 𝑤ℎ𝑒𝑛 𝑥 ≥ 0,
−𝑥, 𝑤ℎ𝑒𝑛 𝑥 < 0
𝑥
𝑦
5 3 0 −3 −5
5 3 0 3 5
𝒚 = 𝒙

13. Graph of 𝑦 = 𝑥

14. Graph of 𝑦 = − 𝑥

15. 𝑥 =
𝑥, 𝑤ℎ𝑒𝑛 𝑥 ≥ 0,
−𝑥, 𝑤ℎ𝑒𝑛 𝑥 < 0
𝑥
𝑦
5 3 0 −3 −5
−5 −3 0 −3 -5
𝒚 = − 𝒙

16. Graph of 𝑦 = − 𝑥

19. 6.1 Graph of the function 𝑦 = 𝑥 − ℎ + 𝑘
Example 1. 𝑦 = 𝑥 − 5 + 2
𝑥
𝑦
3 4 5 6 7
4 3 2 3 4

20. 6.2 Graph of the function 𝑦 = − 𝑥 − ℎ + 𝑘
Example 2. 𝑦 = − 𝑥 + 5 − 1
𝑥
𝑦
−7 −6 −5 −4 −3
-3 −2 −1 −2 −3

21. Exercise 6.1
1. Compare the graphs of the following functions to the graph of 𝑦 = 𝑥 .
(a) 𝑦 = 𝑥 − 3 − 2 (b) 𝑦 = 𝑥 + 1 + 3 (c) 𝑦 = 𝑥 − 2 + 3
2. Compare the graphs of the following functions to the graph of 𝑦 = − 𝑥 .
. (a) 𝑦 = − 𝑥 + 3 + 2 (b) 𝑦 = − 𝑥 − 4 + 1 (c) 𝑦 = − 𝑥 + 4 − 1

22. 6.3 Graph of the function 𝑦 = 𝑎 𝑥
𝑦 = 𝑥
𝑦 = 2 𝑥
𝑦 =
1
2
𝑥
𝑦 = 𝑥
𝑦 = −2 𝑥
𝑦 = − 𝑥
𝑦 = − 𝑥
𝑦 = −
1
2
𝑥

23. 6.4 Graph of the function 𝑦 = 𝑎 𝑥 − ℎ + 𝑘
Example 3. 𝑦 = 2 𝑥 − 5 + 1
𝑦 = 2 𝑥 − 5 + 1
𝑦 = 2 𝑥

24. 6.4 Graph of the function 𝑦 = 𝑎 𝑥 − ℎ + 𝑘
Example 4. 𝑦 = −
1
2
𝑥 + 1 + 3
𝑦 = −
1
2
𝑥 + 1 + 3
𝑦 = −
1
2
𝑥

25. Features of the graph 𝑦 = 𝑎 𝑥 − ℎ + 𝑘
 vertex: (ℎ, 𝑘)
 axis of symmetry: 𝑥 = ℎ
 domain= 𝑡ℎ𝑒 𝑠𝑒𝑡 ℝ 𝑜𝑓 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
 range=
𝑦 𝑦 ≥ 𝑘 𝑤ℎ𝑒𝑛 𝑎 > 0
𝑦 𝑦 ≤ 𝑘 𝑤ℎ𝑒𝑛 𝑎 < 0

𝑤ℎ𝑒𝑛 𝑎 > 0, 𝑘 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑦
𝑤ℎ𝑒𝑛 𝑎 < 0, 𝑘 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑦

26. Exercise 6.2
1. Draw the graph of each of the following functions. Find also vertex,
axis of symmetry, and range of each of the functions.
(1) 𝑦 = 𝑥 + 3 (2) 𝑦 = − 𝑥 + 3 − 2 (3) 𝑦 = 3 𝑥 − 4 +1
. (4) 𝑦 = −
1
2
𝑥 + 3 (5) 𝑦 =
1
2
𝑥 − 4 + 1 (6) 𝑦 = −
1
2
𝑥 − 3 − 1

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