Week 2 - Functions.pptx PDF

GENERAL MATHEMATIC S Ms. Rose Ann P. Ramos, LPT Learning Facilitator Opening Prayer Almighty Father, we praise and thank you for the opportunity to learn today from our facilitator and from one another. Help us to focus our hearts and minds on what we are about to learn in this Inspire...

GENERAL MATHEMATIC S Ms. Rose Ann P. Ramos, LPT Learning Facilitator Opening Prayer Almighty Father, we praise and thank you for the opportunity to learn today from our facilitator and from one another. Help us to focus our hearts and minds on what we are about to learn in this Inspire us by your Holy Spirit so that we may understand the lessons, and see its practical application in our everyday activities. Guide us by your eternal light as we discover more truths about the world around us. We ask this through the GOOD MORNING, EVERYONE! Find my Rectangle Parallelogra m Square Kite Trapezoi d Rhombu 𝟐 Composite number 𝟒 Even number 𝟏𝟏 Odd number 𝟏𝟓 Prime number 𝟐𝟏  𝟐 Even Trapezoi Prime number number d 𝟒 Even Rhombu Composite number s number Odd 𝟏𝟏 Prime number number Kite Odd 𝟏𝟓 Composite number number Parallelogra Odd m 𝟐𝟏 Composite number Function s and Relations Learning Outcomes: At the end of the week, the students should be able to: a.define function; b.differentiate function from relation; c.explain the different characteristics of function; d.evaluate a function; e.determine if the given is function or not by applying the different methods; f. graph a function using graphing paper and Geogebra; and A relation is a set of ordered pairs. The domain of a relation is the set of first coordinates, while range is the set of second coordinates. Domai Rang Domai Rang  𝟐 Even Trapezoi Prime number number d 𝟒 Even Rhombu Composite number s number Odd 𝟏𝟏 Prime number number Kite Odd 𝟏𝟓 Composite number number Parallelogra Odd m 𝟐𝟏 Composite number  A function is a relation in which each elements of the domain corresponds to exactly one element of the range. Domai Rang n e  A relation A relation which is not a which is a function. function. A relation A relation which is a which is not a  All functions are relations, but not all relations are Characteristics of a function: X Y 1. Each element of X 1 A must be assigned to an 2 B element of Y. Y 2. Some elements of Y X A may not be an image of 1 B an element of X. 2 C  X Y 3. Two or more elements 1 A of X may be assigned to 2 B the same element of Y. 3 C X Y 4. An element of X 1 A cannot be assigned to 2 B two or more different 3 C elements of Y. Representation of a function: A function can be represented by: Mapping Diagram Set of Ordered Pairs {(2,1) ,(7 ,4) ,(−3,1),(9,−4)} Table Graph  Vertical Line Test: A set of points in a coordinate plane is the graph of y as a function of x if and only if no vertical line intersects the graph at more than one point.  Go to kahoot. Evaluating a function: 𝒇 ( 𝒙 ) =𝟑 𝒙 𝒊𝒇 𝒙 =𝟒 ; 𝒙 =− 𝟔 𝒊𝒇 𝒙=𝟒 : 𝒊𝒇 𝒙=−𝟔 : 𝒇 ( 𝒙 ) =𝟑 𝒙 𝒇 ( 𝒙 ) =𝟑 𝒙 𝒇 ( 𝟒 ) =𝟑(𝟒) 𝒇 ( − 𝟔 ) =𝟑(− 𝟔) 𝒇 ( 𝟒 ) =𝟏𝟐 𝒇 ( − 𝟔 ) =− 𝟏𝟖  𝟐 𝒇 ( 𝒃 ) =𝒃 − 𝟕 𝒃 𝒊𝒇 𝒃=− 𝟓 ; 𝒃=𝟑 𝒃 𝒊𝒇 𝒃=−𝟓 : 𝒊𝒇 𝒃=𝟑 𝒃: 𝟐 𝟐 𝒇 ( 𝒃 ) =𝒃 − 𝟕 𝒃 𝒇 ( 𝒃 ) =𝒃 − 𝟕 𝒃 𝟐 𝟐 𝒇 ( −𝟓 )=(−𝟓) −𝟕 (−𝟓) 𝒇 ( 𝟑 𝒃 ) =(𝟑 𝒃) −𝟕(𝟑 𝒃) 𝒇 ( − 𝟓 )=𝟐𝟓+𝟑𝟓 𝟐 𝒇 ( 𝟑 𝒃 ) =𝟗 𝒃 −𝟐𝟏 𝒃 𝒇 ( − 𝟓 )=𝟔𝟎  TRY THIS! 𝑓 ( 𝑥 ) =12 𝑥+ 3 a.) x = 4 b.) x = -9 c.) x =0 2 𝑓 ( 𝑥 ) =3 𝑥 − 15 a.) x = 3 b.) x = -1 c.) x = 4 𝑓 ( 𝑥 ) =12 𝑥+ 3 𝒇 ( 𝟒 ) =𝟓𝟏 𝒇 ( − 𝟗 )=− 𝟏𝟎𝟓 𝒇 ( 𝟎 ) =𝟑 2 𝑓 ( 𝑥 ) =3 𝑥 − 15 𝒇 ( 𝟑 )=𝟏𝟐 𝒇 ( − 𝟏 )=− 𝟏𝟐 𝒇 ( 𝟒 ) =𝟑𝟑 Functions in Real Life: Mikha is a cashier in a small grocery having a daily salary of What is her salary for the month if she worked for 22 days? 𝒊𝒏𝒑𝒖𝒕 :𝒍𝒆𝒕 𝒙 𝒃𝒆𝒕𝒉𝒆 𝒏𝒐. 𝒐𝒇 𝒅𝒂𝒚𝒔 𝒇 ( 𝒙 ) =𝟓𝟖𝟓 ( 𝒙 ) 𝒇 ( 𝟐𝟐 ) =𝟓𝟖𝟓( 𝟐𝟐) 𝒇 ( 𝟐𝟐 ) =𝟏𝟐 , 𝟖𝟕𝟎 Functions in Real Life: Aiah walks at the speed of 7km/hr. Find the distance covered if she walks for 3 hours. 𝒊𝒏𝒑𝒖𝒕 :𝒍𝒆𝒕 𝒙 𝒃𝒆𝒕𝒉𝒆 𝒏𝒐. 𝒐𝒇 𝒉𝒐𝒖𝒓𝒔 𝒇 ( 𝒙 ) =𝟕( 𝒙 ) 𝒇 ( 𝟑 )= 𝟕(𝟑) 𝒇 ( 𝟑 )= 𝟐𝟏 Functions in Real Life: A ball is dropped from a 75m building. The height (in m.) after t seconds is Find its height from the ground after 5 seconds. 𝒊𝒏𝒑𝒖𝒕 :𝒍𝒆𝒕 𝒕 𝒃𝒆𝒕𝒉𝒆 𝒏𝒐. 𝒐𝒇 𝒔𝒆𝒄𝒐𝒏𝒅𝒔 𝟐 𝒉 ( 𝒕 ) =𝟓.𝟖 𝒕 +𝟕𝟐 𝟐 𝒉 ( 𝟓 ) =𝟓. 𝟖( 𝟓) +𝟕𝟐 𝒉 ( 𝟓 ) =𝟐𝟏𝟕  TRY THIS! 1. The function A described by gives the area of an equilateral triangle with side s. a. Find the area when a side measures 8 cm. b. Find the area when a side measures 16 cm. 2. The function C described by gives the Celsius temperature corresponding to the Fahrenheit temperature F. a. Find the C temperature equivalent to b. Find the C temperature equivalent to. Answer the given items on a paper and send it thru G-chat. Operatio ns on Function Sum: Difference: Product: Quotient: Sum of Let f and g be two functions with overlapping domains. Then for all x common to both domains, the sum of f and g is defined as:  Given and , find. ( 𝑓 + 𝑔 ) ( 𝑥 )=( 3 𝑥 − 3 ) +(10 𝑥 +4) ( 𝒇 + 𝒈 ) ( 𝒙 )= 𝟏𝟑 𝒙 +𝟏 Given and Find. ( 𝑓 + 𝑔 ) ( 𝑥 )=( 8 𝑥 +2 𝑥 − 5 ) +( 𝑥 +2) 2 2 ( 𝒇 + 𝒈 ) ( 𝒙 )= ¿ Given and Find then evaluate the sum when. ( 𝑓 + 𝑔 ) ( 𝑥 )=( 4 𝑥 − 2 𝑥+1 ) +(7 𝑥 − 3) 2 3 ( 𝒇 + 𝒈 ) ( 𝒙 )= ¿ Evaluate: when 3 2 ( 𝑓 + 𝑔 ) ( 5 ) =7 𝑥 + 4 𝑥 − 2 𝑥 − 2 3 2 ( 𝑓 + 𝑔 ) ( 5 ) =7(5) + 4(5) − 2(5) − 2 ( 𝒇 + 𝒈 ) ( 𝟓 ) =𝟗𝟔𝟑 Difference of Let f and g be two functions with overlapping domains. Then for all x common to both domains, the difference of f and g is defined as:  Given and , find. 2 ( 𝑓 − 𝑔 ) ( 𝑥 ) =( 𝑥 − 1 ) − (6 𝑥 +2 𝑥+ 4) 𝟐 ( 𝒇 − 𝒈 ) ( 𝒙 ) =− 𝟔 𝒙 − 𝒙 − 𝟓  Given and Find. ( 𝑓 − 𝑔 ) ( 𝑥 ) =( 15 𝑥 − 2 𝑥 − 10 ) −( 𝑥 +8) 2 ( 𝒇 − 𝒈 ) ( 𝒙 ) =¿  Given and Find then evaluate the difference when. 2 ( 𝑓 − 𝑔 ) ( 𝑥 ) =( 3 𝑥+7 ) − ( 𝑥 − 2 𝑥+9) ( 𝒇 + 𝒈 ) ( 𝒙 )= ¿ Evaluate: when 2 ( 𝑓 − 𝑔 ) ( 4 ) =− 𝑥 + 5 𝑥 − 2 2 ( 𝑓 − 𝑔 ) ( 4 ) =−( 4) +5( 4)− 2 ( 𝒇 − 𝒈 ) ( 𝟒 ) =𝟐 Product of Let f and g be two functions with overlapping domains. Then for all x common to both domains, the product of f and g is defined as:  Given and , find. ( 𝑓𝑔 ) ( 𝑥 )= ( 3 𝑥 − 4 ) (𝑥 +8) 2 ( 𝑓𝑔 )( 𝑥 )=3 𝑥 +24 𝑥 − 4 𝑥 − 32 𝟐 ( 𝒇𝒈 ) ( 𝒙 ) =𝟑 𝒙 +𝟐𝟎 𝒙 − 𝟑𝟐 Given and , find. ( 𝑓𝑔 ) ( 𝑥 )= ( 5 𝑥 + 𝑥 +3 ) (2 𝑥+1) 2 ( 𝑓𝑔 ) ( 𝑥 ) = ¿ ( 𝒇𝒈 ) ( 𝒙 ) =¿  Given and Find then evaluate the product when. 2 ( 𝑓𝑔 ) ( 𝑥 )= ( 6 𝑥 − 5 ) ( 4 𝑥 +2 𝑥+9) ( 𝑓𝑔 ) ( 𝑥 ) = ¿ ( 𝒇𝒈 ) ( 𝒙 ) =¿ Evaluate: when 3 2 ( 𝑓𝑔 )( − 2 )=24 𝑥 − 8 𝑥 +44 𝑥 − 45 3 2 ( 𝑓𝑔 )( − 2 )=24 (− 2) − 8 ( − 2 ) + 44( − 2) − 45 ( 𝒇𝒈 ) ( − 𝟐 )=− 𝟑𝟓𝟕 Quotient of Let f and g be two functions with overlapping domains. Then for all x common to both domains, the quotient of f and g is defined as:  Given and Find. ( 𝑥 +2 ) ( 𝑥 − 4) ( 𝑓 / 𝑔) ( 𝑥 ) = ( 𝑥 − 5) ( 𝑥 − 4 ) 𝒙+𝟐 ( 𝒇 / 𝒈 ) ( 𝒙 )= 𝒙 −𝟓  Given and Find. 2 𝑥 +5 𝑥 − 24 ( 𝑥 − 3) ( 𝑓 / 𝑔) ( 𝑥 ) = 2 ( 𝑓 / 𝑔) ( 𝑥 ) = 𝑥 +6 𝑥 − 16 ( 𝑥 − 2) 𝒙 −𝟑 ( 𝒇 / 𝒈 ) ( 𝒙 )= 𝒙 −𝟐 ACTIVITY #1: (20 pts.) Create your own example for each operations on functions. Solve the examples that you created. Do this activity on a yellow paper.