Week-2-Operation-on-Functions-Genmathg11

Grade 11 genmath

2. •Identify the different operation on functions.
•Solve problems involving functions
•Define piecewise function

3. Piecewise
Prepared by: Mr. Dane Andrei V. Aguinaldo

4. A function defined by multiple
subfunctions, where each
subfunction applies to a certain
interval of the main function’s
domain.

5. ??????�??????�����:
&#3627408519;(??????)= ?????? + &#3627409361; &#3627408522;&#3627408519; ?????? < −&#3627409361;
??????=−&#3627409363;
&#3627408519;(−&#3627409363;) = −&#3627409363; +&#3627409361;
&#3627408519;−&#3627409363;=−&#3627409360;

6. ??????&#3627408528;??????&#3627408534;&#3627408533;&#3627408522;&#3627408528;&#3627408527;:
&#3627408519;??????= &#3627409360;?????? – &#3627409361;
&#3627408522;&#3627408519; −&#3627409361;≤??????≤&#3627409363;,??????=&#3627409360;
&#3627408519;&#3627409360;=&#3627409360;&#3627409360;−&#3627409361;
&#3627408519;&#3627409360;=−&#3627409359;
&#3627408519;&#3627409360;=&#3627409362;−&#3627409361;

7. ??????&#3627408528;??????&#3627408534;&#3627408533;&#3627408522;&#3627408528;&#3627408527;:
&#3627408519;??????= ??????
&#3627409360;
−&#3627409359; &#3627408522;&#3627408519; ??????>&#3627409363;
&#3627408519;&#3627409364;=(&#3627409364;)
&#3627409360;
−&#3627409359;
&#3627408519;&#3627409364;=&#3627409361;&#3627409363;
&#3627408519;&#3627409364;=&#3627409361;&#3627409364;−&#3627409359;
x = 6

8. Operation on
Prepared by: Mr. Dane Andrei V. Aguinaldo

9. Directions:
1. Each student is holding four shapes namely; triangle,
square, circle and rectangle.
3. Each question must be answered within 15 seconds.
After the timer, students need to raise their chosen
shape.
2. All of the student must stand and those who will get
the wrong answer will sit down.
4. Student that will remain standing after finishing all of
the questions will get a plus 10 points in recitation.

10. &#3627409361;??????
&#3627409360;
−&#3627409360;??????+&#3627409362;?????? −&#3627409362;
&#3627409363;??????−&#3627409362;&#3627409363;??????
&#3627409360;
−&#3627409362;
&#3627409361;??????
&#3627409360;
−&#3627409360;??????−&#3627409362;&#3627409361;??????
&#3627409360;
+&#3627409360;??????−&#3627409362;

11. (&#3627409360;??????
&#3627409360;
+&#3627409362;)−(−&#3627409362;??????
&#3627409360;
+??????)
−&#3627409360;??????
&#3627409360;
−??????+&#3627409362;&#3627409364;??????
&#3627409360;
−??????+&#3627409362;
&#3627409365;??????
&#3627409360;
+&#3627409362;−??????
&#3627409360;
−&#3627409362;

12. (??????
&#3627409360;
−&#3627409359;)(&#3627409360;??????)
&#3627409360;??????
&#3627409360;
−&#3627409360;????????????
&#3627409361;
−&#3627409360;??????
&#3627409360;??????
&#3627409361;
−&#3627409360;????????????
&#3627409360;
−&#3627409360;??????

13. &#3627409362;??????
&#3627409363;
÷&#3627409360;??????
&#3627409362;??????
&#3627409363;
&#3627409360;??????
&#3627409362;
&#3627409360;??????
&#3627409363;
&#3627409362;??????
&#3627409362;

14. &#3627408493;??????&#3627408516;&#3627408533;&#3627408528;??????:??????
&#3627409360;
−??????−&#3627409364;
(??????−&#3627409364;)(??????+&#3627409359;) (??????−&#3627409361;)(??????+&#3627409360;)
(??????+&#3627409364;)(??????−&#3627409359;) (??????−&#3627409360;)(??????+&#3627409361;)

15. (a) Their sum, denoted by &#3627408519;+&#3627408520;, is the function
defined by &#3627408519;+&#3627408520;??????=&#3627408519;??????+&#3627408520;(??????).
(b) Their difference, denoted by &#3627408519;−&#3627408520;, is the
function defined by &#3627408519;−&#3627408520;??????=&#3627408519;??????−&#3627408520;(??????).

16. (c) Their product, denoted by &#3627408519;∙&#3627408520;, is the function
defined by &#3627408519;∙&#3627408520;??????=&#3627408519;??????∙&#3627408520;(??????).
(d) Their quotient, denoted by
&#3627408519;
&#3627408520;
, is the function
defined by (
&#3627408519;
&#3627408520;
)??????=
&#3627408519;(??????)
&#3627408520;(??????)
.

17. &#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527; &#3627408533;&#3627408521;??????&#3627408533; &#3627408519;??????=&#3627409360;?????? −&#3627409361; ??????&#3627408527;&#3627408517; &#3627408520;??????=&#3627409361;??????+&#3627409365;
&#3627408519;+&#3627408520;??????=&#3627408519;??????+&#3627408520;(??????)
=(&#3627409360;?????? −&#3627409361;)+
=&#3627409360;?????? −&#3627409361;+&#3627409361;??????+&#3627409365;
=&#3627409363;??????
∴(&#3627408519;+&#3627408520;)(??????)=&#3627409363;??????+&#3627409362;
(&#3627409361;??????+&#3627409365;)
+ &#3627409362;

18. &#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527; &#3627408533;&#3627408521;??????&#3627408533; &#3627408519;??????=&#3627409365;??????
&#3627409360;
−&#3627409361;?????? ??????&#3627408527;&#3627408517; &#3627408520;??????=&#3627409361;??????
&#3627409360;
+&#3627409360;??????
&#3627408519;−&#3627408520;??????=&#3627408519;??????−&#3627408520;(??????)
=&#3627409365;??????
&#3627409360;
−&#3627409361;??????−
=&#3627409365;??????
&#3627409360;
−&#3627409361;??????
=&#3627409362;??????
&#3627409360;
∴&#3627408519;−&#3627408520;??????=&#3627409362;??????
&#3627409360;
−&#3627409363;??????
−&#3627409361;??????
&#3627409360;
−&#3627409360;??????
(&#3627409361;??????
&#3627409360;
+&#3627409360;??????)
−&#3627409363;??????

19. &#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527; &#3627408533;&#3627408521;??????&#3627408533; &#3627408519;??????=??????+&#3627409361; ??????&#3627408527;&#3627408517; &#3627408520;??????=??????+&#3627409363;
&#3627408519;∙&#3627408520;??????=&#3627408519;??????∙&#3627408520;(??????)
=??????+&#3627409361;(??????+&#3627409363;)
∴&#3627408519;∙&#3627408520;??????=??????
&#3627409360;
+&#3627409366;??????+&#3627409359;&#3627409363;
=??????
&#3627409360;
+
=????????????+??????&#3627409363;+&#3627409361;??????+&#3627409361;(&#3627409363;)
&#3627409363;??????+&#3627409361;??????+&#3627409359;&#3627409363;

20. &#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527; &#3627408533;&#3627408521;??????&#3627408533; &#3627408519;??????=&#3627409366;?????? −&#3627409360; ??????&#3627408527;&#3627408517; &#3627408520;??????=&#3627409362;??????−&#3627409359;
&#3627408519;
&#3627408520;
??????=
&#3627408519;(??????)
&#3627408520;(??????)
∴
&#3627408519;
&#3627408520;
??????=&#3627409360;
=
&#3627409366;??????−&#3627409360;
&#3627409362;??????−&#3627409359;
=
&#3627409360;(&#3627409362;??????−&#3627409359;)
&#3627409362;??????−&#3627409359;
=
&#3627409360;
&#3627409359;

21. •&#3627408518;??????=?????? −&#3627409360;
•&#3627408519;??????=&#3627409364;??????+&#3627409362;
•&#3627408520;??????=&#3627409361;??????
&#3627409360;
+&#3627409360;??????
•&#3627408521;??????=??????
&#3627409360;
−&#3627409362;??????+&#3627409362;
•&#3627408522;??????=&#3627409360;??????
&#3627409360;
−&#3627409362;
&#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527;: &#3627408493;&#3627408522;&#3627408527;&#3627408517;:
&#3627409359;.(&#3627408522;+&#3627408520;)(??????)
&#3627409360;.(&#3627408520;−&#3627408519;)(??????)
&#3627409361;.(&#3627408518;∙&#3627408519;)(??????)
4.
&#3627408521;
&#3627408518;
(??????)

22. •&#3627408518;??????=?????? −&#3627409360;
•&#3627408519;??????=&#3627409364;??????+&#3627409362;
•&#3627408520;??????=&#3627409361;??????
&#3627409360;
+&#3627409360;??????+&#3627409360;
•&#3627408521;??????=??????
&#3627409360;
−&#3627409362;??????+&#3627409362;
•&#3627408522;??????=&#3627409360;??????
&#3627409360;
−&#3627409362;
&#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527;:
&#3627409359;.(&#3627408522;+&#3627408520;)(??????)
&#3627408522;+&#3627408520;??????=&#3627408522;??????+&#3627408520;(??????)
=(&#3627409360;??????
&#3627409360;
−&#3627409362;)+(&#3627409361;??????
&#3627409360;
+&#3627409360;??????+&#3627409360;)
=&#3627409360;??????
&#3627409360;
−&#3627409362;+&#3627409361;??????
&#3627409360;
+&#3627409360;??????+&#3627409360;
=&#3627409363;??????
&#3627409360;
−&#3627409360;+&#3627409360;??????
&#3627408522;+&#3627408520;??????= &#3627409363;??????
&#3627409360;
+&#3627409360;??????−&#3627409360;

23. •&#3627408518;??????=?????? −&#3627409360;
•&#3627408519;??????=&#3627409364;??????+&#3627409362;
•&#3627408520;??????=&#3627409361;??????
&#3627409360;
+&#3627409360;??????+&#3627409360;
•&#3627408521;??????=??????
&#3627409360;
−&#3627409362;??????+&#3627409362;
•&#3627408522;??????=&#3627409360;??????
&#3627409360;
−&#3627409362;
&#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527;:
&#3627409360;.(&#3627408520;−&#3627408519;)(??????)
&#3627408520;−&#3627408519;??????=&#3627408520;??????−&#3627408519;(??????)
=(&#3627409361;??????
&#3627409360;
+&#3627409360;??????+&#3627409360;)−(&#3627409364;??????+&#3627409362;)
=&#3627409361;??????
&#3627409360;
+&#3627409360;??????+&#3627409360;−&#3627409364;??????−&#3627409362;
=&#3627409361;??????
&#3627409360;
−&#3627409362;??????−&#3627409360;
&#3627408520;−&#3627408519;??????=&#3627409361;??????
&#3627409360;
−&#3627409362;??????−&#3627409360;

24. •&#3627408518;??????=?????? −&#3627409360;
•&#3627408519;??????=&#3627409364;??????+&#3627409362;
•&#3627408520;??????=&#3627409361;??????
&#3627409360;
+&#3627409360;??????+&#3627409360;
•&#3627408521;??????=??????
&#3627409360;
−&#3627409362;??????+&#3627409362;
•&#3627408522;??????=&#3627409360;??????
&#3627409360;
−&#3627409362;
&#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527;:
&#3627409361;.(&#3627408519;∙&#3627408518;)(??????)
&#3627408519;∙&#3627408518;??????=&#3627408519;??????∙&#3627408518;(??????)
=??????−&#3627409360;(&#3627409364;??????+&#3627409362;)
=??????&#3627409364;??????+??????&#3627409362;+−&#3627409360;&#3627409364;??????+−&#3627409360;(&#3627409362;)
=&#3627409364;??????
&#3627409360;
+&#3627409362;??????−&#3627409359;&#3627409360;??????−&#3627409366;
&#3627408519;∙&#3627408520;??????=&#3627409364;??????
&#3627409360;
−&#3627409366;??????−&#3627409366;

25. •&#3627408518;??????=?????? −&#3627409360;
•&#3627408519;??????=&#3627409364;??????+&#3627409362;
•&#3627408520;??????=&#3627409361;??????
&#3627409360;
+&#3627409360;??????+&#3627409360;
•&#3627408521;??????=??????
&#3627409360;
−&#3627409362;??????+&#3627409362;
•&#3627408522;??????=&#3627409360;??????
&#3627409360;
−&#3627409362;
&#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527;:
4.(
&#3627408521;
&#3627408518;
)(??????)
&#3627408521;
&#3627408518;
??????=
&#3627408521;(??????)
&#3627408518;(??????)
&#3627408521;
&#3627408518;
??????=??????−&#3627409360;
=
??????
&#3627409360;
−&#3627409362;??????+&#3627409362;
??????−&#3627409360;
=
(??????−&#3627409360;)(??????−&#3627409360;)
??????−&#3627409360;

26. The composite function, denoted by (f ∘ g), is
defined by (f ∘ g)(x) = f(g(x))
The process of obtaining a composite function is
called function composition
Note: f(g(x)) is not the same with g(f(x)).

27. &#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527; &#3627408533;&#3627408521;??????&#3627408533; &#3627408519;??????=&#3627409360;?????? −&#3627409361; ??????&#3627408527;&#3627408517; &#3627408520;??????=&#3627409362;??????−&#3627409359;.&#3627408493;&#3627408522;&#3627408527;&#3627408517;&#3627408519;∘&#3627408520;??????
&#3627408519;∘&#3627408520;??????=&#3627408519;(&#3627408520;??????)
∴&#3627408519;∘&#3627408520;??????=&#3627409366;?????? −&#3627409363;
=&#3627409360;&#3627409362;??????−&#3627409359;−&#3627409361;
=&#3627409366;??????− &#3627409360;− &#3627409361;
=&#3627409366;?????? −&#3627409363;

28. &#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527; &#3627408533;&#3627408521;??????&#3627408533; &#3627408519;??????=&#3627409360;?????? −&#3627409361; ??????&#3627408527;&#3627408517; &#3627408520;??????=&#3627409362;??????−&#3627409359;.????????????????????????&#3627408520;∘&#3627408519;??????
&#3627408520;∘&#3627408519;??????=&#3627408520;(&#3627408519;??????)
∴&#3627408519;∘&#3627408520;??????=&#3627409366;?????? −&#3627409359;&#3627409361;
=&#3627409362;&#3627409360;??????−&#3627409361;−&#3627409359;
=&#3627409366;??????− &#3627409359;&#3627409360;− &#3627409359;
=&#3627409366;?????? −&#3627409359;&#3627409361;

29. •&#3627408518;??????=?????? −&#3627409360;
•&#3627408519;??????=&#3627409364;??????+&#3627409362;
•&#3627408522;??????=??????
&#3627409360;
−&#3627409362;
&#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527;:
&#3627409359;.(&#3627408519;∘&#3627408518;)(??????)
(&#3627408519;∘&#3627408518;)??????=&#3627409364;??????−&#3627409366;
&#3627408519;∘&#3627408518;??????=&#3627408519;(&#3627408518;??????)
=&#3627409364;??????−&#3627409360;+&#3627409362;
=&#3627409364;??????−&#3627409359;&#3627409360;+&#3627409362;
=&#3627409364;??????−&#3627409366;

30. •&#3627408518;??????=?????? −&#3627409360;
•&#3627408519;??????=&#3627409364;??????+&#3627409362;
•&#3627408522;??????=??????
&#3627409360;
−&#3627409362;
&#3627408494;&#3627408522;&#3627408535;&#3627408518;&#3627408527;:
2.(&#3627408522;∘&#3627408518;)(??????)
(&#3627408522;∘&#3627408518;)??????=??????
&#3627409360;
−&#3627409362;??????
&#3627408522;∘&#3627408518;??????=&#3627408522;(&#3627408518;??????)
=(?????? −&#3627409360;)
&#3627409360;
−&#3627409362;
=??????
&#3627409360;
−&#3627409362;??????+&#3627409362;−&#3627409362;
=??????
&#3627409360;
−&#3627409362;??????

31. Kamao Network charges ₱500 monthly cable
connection fee plus ₱125 for each hour of pay-
per-view (PPV) event regardless of a full hour or
a fraction of an hour. Represent the given into a
function equation.
f(x) = Php 125x + Php 500

32. a. What is the monthly bill of a customer who
watched 25 hours of PPV events?
f(x) = Php 125x + Php 500
f(25) = Php 125(25) + Php 500
= Php 3,125 + Php 500
f(25) = Php 3,625
The monthly bill of a customer who watched 25 hours
of PPV events can be represented by 24<x≤25

33. b. What is the monthly bill of a customer who
watched 12.1 hours of PPV events?
f(x) = Php 125x + Php 500
f(13) = Php 125(13) + Php 500
= Php 1,625 + Php 500
f(13) = Php 2,125
The monthly bill of a customer who watched 12.1
hours of PPV events can be represented by 12<x≤13

34. c. What is the monthly bill of a customer who
watched 0.2 hours of PPV events?
f(x) = Php 125x + Php 500
f(1) = Php 125(1) + Php 500
= Php 125 + Php 500
f(11) = Php 625
The monthly bill of a customer who watched 0.2 hours
of PPV events can be represented by 0<x≤1