Please help Since functions convert the value of an input variable into the value of an output variable, it stands to re

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Please help
Since functions convert the value of an input variable into the value of an output variable, it stands to reasonthat this output could then be used as an input to a second function. This process is known as composition offunctions, in other words, combining the action or rules of two functions.Exercise #1: A circular garden with a radius of 15 feet is to be covered with topsoil at a cost of $1.25 persquare foot of garden space.
In this exercise, we see that the output of an area function is used as the input to a cost function. This idea canbe generalized to generic functions, f and g as shown in the diagram below.
There are two notations that are used to indicate composition of two functions. These will be introduced in thenext few exercises, both with equations and graphs.Exercise #2: Given   2 f x x gx x   5 and 2 3 , find values for each of the following.(a) f g    1  (b) g f   2  (c) g g 0 
(d)    f g   2 (e)   g f  3  (f)  f f  1 (a) Determine the area of this garden to thenearest square foot.
(b) Using your answer from (a), calculate thecost of covering the garden with topsoil.
Input = x f g
Output from fbecomes the input to g Final output = y
COMMON CORE ALGEBRA II, UNIT #2 – FUNCTIONS AS CORNERSTONES OF ALGEBRA II – LESSON #3
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
Exercise #3: The graphs below are of the functions y f x y gx     and  . Evaluate each of the followingquestions based on these two graphs.
(a) g f     2  (b) f g 1  (c) g g    1 
(d)    g f    2 (e)  f g 0  (f)    f f  0 
On occasion, it is desirable to create a formula for the composition of two functions. We will see this facet ofcomposition throughout the course as we study functions. The next two exercises illustrate the process offinding these equations with simple linear and quadratic functions.Exercise #4: Given the functions f x x gx x     3 2 and 5 4   , determine formulas in simplest y ax b  form for:(a) f   g x  (b) gfx   
Exercise #5: If   2 f x x gx x   and 5 then f gx    (1) 2x  25 (3) 2x  5
(2) 2x  25 (4) 2
x x   10 25v
Name Since functions convert the value of an input varuble in the value of an output variable, stand that this output could then be used as an input so a second function. This process is known as position of functions in other words, combining the action or rules of two fonction Exce: A circular garden with a ralios of 15 ft is to be covered with splat act of $1.25 per square foot of garden space (a) Determine the wes of this to the square fo Inpat FUNCTION COMPOSITION COMMON CORE ALGERRA II 3 this exercise we see that the output of an area function is and as the input to a co This com the generatogenic functions, and gas shown in the diagram be (d) (-2)(-2)- 00/(2)) There are two notations that are used to indicate composition of two functions. These will be in the next few exercises, both with equations and graph Exec 2: ()--5 and g()-2-3, find values for each of the following (10) 60) (-/-) Ourut be becomes the input ++/0) Date in (g) M Ex 43: The graphs below are of the functions y/(a) andy-g(s). Evalute cach of the Sllowing of covering the garden with sp do /((-))- (0) (-2)(0)- (/-/)(-1)- so ex- 152/-/30- On occasion, it is desirable to create a formala for the composition of two ens We will see that of composition throughout the counse as we study functions. The next twees the posof finding these equations with simple linear and quadratic function
MO 4 of 4 (((-2)) A The graphs of y(x) andykis) are shown below. Evaluate the following hand on these two graph AN COCA-C Mond 4. If g)-3-5 and h()-2-4 thn (g)(x)=7 (1) 6x-17 (2) 6-14 (2.9 (²21 (-x)(38) (ho (-A)(0) (1):54 (2)84 5. If(x)+5(x)=x+4h/(())- (0) 4x²+20 (4) x-1 APPLICATIONS 128-² 6. Scientists modeled the intensity of the sun, as a function of the number of hours 6:00 aming the function (4) They the model the temperature of the soil. T, as a function of the intensity wing the function (1)-√50007. Which of the following is closest to the temperature of the wil at 2:00 (167 Co ((x-4)(0) 404(4-2)) 7. Physics students are studying the effect of the temperature 7, on the speed of wend. 5 They that the speed of sound in meter per second is a function of the temper is degs Kelvin Kh S(K) 40K The degrees Kelvis is a function of the temperate in Ceb K(C) C-27315. Find the speed of wound when the temperatures 30 degrees Cold to the REASONING Consider the functions (*)-2-4 and g()-the g (g(/(15)) (g((-3)) (4) What appears to always be true when you compose these two function E-Fonctions 45-Coreene
Ex: The graphs below are of the factions y/(s) andy-g(). Evalute each of the sidewing questions based on these two graph () g(/(2))- (d) (x-7)(-2) (1²-25 2²-25 00/(-1)- On occasion, it is desirable to create a formals for the composition of two functions. We will see this composition throughout the course as we staly fections. The next two exercises finding these options with simple linear and quadratication the Exercise #4: Given the functions/(x)-38-2 and g(x)-5-4, determine forma in sployab Exce/(x) and g(s)-x-5 h /(())- (6)(x-1(6) (e) (f+x)(0) 64A(4(0)) (x²-5 (4)²-10-25 Marabo FLUENCY 1. Geven f(x)=3-4 and g(x)=-27 evaluate (/(2(0)) (/(-2)) 2. Given 4()-11-2 Ale(18)) FUNCTION COMPOSITION COMMON CORE ALGEBRA II HOMEWORK in) (f-g)(5) (()) (((4)) -ats) (e) (6-(38) 10/0/00) Dete (x-x)(2) ( 40 (-X) (0 (-6)(0) of sof 3. The graph of y(x) andy) are shown below. Exalate the following hed on these two graph
(0) M(g(18)) (4) h(A(0)) (a) ((-2)) (c) (-2)(38) 3. The graphs of y(x) and y(s) are shown below. Evaluate the following based on these two graphs. (b) (A-A)(0) 4. g(x)=3x-5 and (x)=2x-4 then (g-A)(x)=7 131 Đang (1) 54 (1) 6-17 (2) 6-14 5. If f(x) +5 and g(x)=x+4 then/(g(x))- (1) ²49 (3) 4x² 20 (2)²+8+21 (4) x² +21 (Ⓒ) (g+g)(11) (0) (-A)(0) CONCORE ALGER 2-FNS CORNERAL-L RBNY 197.COM Mand (3)67 (c) (A(-2)) APPLICATIONS 6. Scientists modeled the intensity of the sun, I, as a function of the number of hours since 6:00 am using the function /(6)-126-4 They then model the temperature of the soil, 7., as a function of the intensity 36 using the function ()-√5000/. Which of the following is closest to the temperature of the soil at 2:00 (d) (-4) (-2) 7. Physics students are studying the effect of the temperature, T, on the speed of sound. 5. They find that the speed of sound in meters per second is a function of the temperature in degrees Kelvin, K. by S(K)√410K The degrees Kelvin is a function of the temperature in Celsius given by K(C)-C+273.15. Find the speed of sound when the temperature is 30 degrees Celsius Round to the nearest wh REASONING X. Consider the functions/(x)=2x+9 and g(x)= Calculate the following (A) 2(/(15)) (b)(/(-3)) (4) What appears to always be true when you compose these two functions? (0 z(/(x))