Inverse Functions and Composition of Functions PDF

(7.1) Inverse Functions and Function Composition (7.2)Inverses of Quadratic and Cubic Functions Learning intention  L.I : Students will find and verify inverse functions and use composition of functions to create new functions. S.C:  1. I can evaluate functions  2. I can find composite functio...

(7.1) Inverse Functions and Function Composition (7.2)Inverses of Quadratic and Cubic Functions Learning intention  L.I : Students will find and verify inverse functions and use composition of functions to create new functions. S.C:  1. I can evaluate functions  2. I can find composite functions.  3. I can use composite functions to solve real life applications  Standard:HSF.BF.A.1Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.  Key words :  Evaluate functions.Composite Functions 2 Warm up Given f(x) 3x  1.Calculate each of the following a) f(2) b) f (5m) c ) f ( 4 x  7) 3  Bell Ringer Math Word Wall- https://wordwall.net/resource/1216183 6 4  Video ( Inverse Function) https://www.hmhco.com/content/math/ common/math_video_player/index.htm l?custom_correlation_id=d52e7c3f-4cd 3-4e96-8dac-35e015e01493&refid=71 41_AI1_en 5  Video ( Khan Academy) Composite https://www.khanacademy.org/math/pr ecalculus/x9e81a4f98389efdf:composi te/x9e81a4f98389efdf:composing/v/ev aluating-composite-functions-example- 1 6  I DO Given f(x) 3 x  4 and g(x) 2 x  3, Calculate the following a) f(2k)  b)g(m  1)  c) (f  g)(x)  b)(g  f )( x)  © 2020 McGraw-Hill Education. 7 5-7  Check understanding ( Use classkick) Given calculate and simplify a) f(1) b) f(x+1) © 2020 McGraw-Hill Education. 8 5-8  WE DO ( Use classkick) a) f(2) b) f(3x) c) d) © 2020 McGraw-Hill Education. 9 5-9 Classkick ( Link & code) P1 (9AG) https://app.classkick.com/login/MGALFF © 2020 McGraw-Hill Education. 10 5-10 Classkick ( Link & code) P1 (9BG) https://app.classkick.com/login/T5Z37 L © 2020 McGraw-Hill Education. 11 5-11 You DO Given f(x) 9 x  4 and g(x) 3 x  10, Calculate the following a) f(2k)  b)g(4m  1)  c) (f  g)(x)  d)(g  f )( x)  e)f(g(2)  f)Challenge : g(f(3x - 1)  © 2020 McGraw-Hill Education. 12 5-12 You DO Real life application : A clothing store is having a “40% off everything” sale. Ted has a $25 gift card. The function T (c) = c - 25 represents Ted’s cost T (in dollars) for items that cost c dollars. The function P(c) = 0.6c represents the purchase price P (in dollars) for items that originally cost c dollars. 1. Use the information from the problem to write Ted’s cost T as a function of the purchase cost P. Then use the function to find Ted’s cost when the original cost of his items is $54. (T o P)(c) = 0.6c - 25; $7.40 write the equation for each composition of functions (f ◦ g)(x) and (g ◦ f ) (x), ( Extra ) © 2020 McGraw-Hill Education. 13 5-13  Challenge 2 3x Given f(x) 2 x  6 , g(x) x and h(x)  x 1 Find ( f  h  g )( x) ( g  f  h)(1) 14  Answer Key Q(6-9) write the equation for each composition of functions (f ◦ g)(x) and (g ◦ f )(x), and express their domains and ranges in set notation ( Extra ) 6) 7) 8) © 2020 McGraw-Hill Education. 15 5-15  Exit Slip (classkick) 𝐺𝑖𝑣𝑒𝑛 𝑡h𝑎𝑡 𝑓 ( 𝑥 ) =2 𝑥 𝑔 ( 𝑥 )=5 𝑥 +1 𝑓𝑖𝑛𝑑( 𝑓 ∘ 𝑔)(𝑥) Go to hmh and solve the assigned exit slip L(7-1& 7- 2)P1 https://www.hmhco.com/ui/#/assignments/?sectionRef Id=c29719f9-b512-42d2-87ba-38ce3d72fc6a&tab=0 16 Reflection: 1.Summarize the key points of the lesson? 2.Which problem did you find the most challenging and why? 3.How confident do you feel about Composite function on a scale of 1 to 5? 17 Closure (5 min) Literacy: Write the key words of the lesson and explain them in your own words. Write on your copybook what did you learn today. 18 Closure (5 min) 1) What did you learn today? 2) What did you remember today? 3) Write all the Key Words of this lesson. 4) Do you have any question regarding This lesson? 19