"9? + 2 ? ? ?1=? = 3 1.Consider the piecewise function ? ? = 8? + 7 ? ? ?3 <? = 66? + 5 ? ? ?6 <? = 9 Calculate f (8). Show some work/explanation.1. 53A.74B. 71C.53D.74, 71, and 53Solution: Given ? = 8; Taking the equation for 6 <? = 9, Therefore replacing ? in the equation ? ? = 6? + 5 = 48 + 5 = 53. 2. Given? ? = ? - 1and ? ? =? - 4, which of the following is the domain of the quotientfunction f / g ? Explain.2.____B__A. -8, 4 ? 4,8 B. [1, 4)?4,8C.1,8 D. 1,8 ? -1 Solution: (f/g)=? -4 The domain for f(x)= ? - 1 is from 1 onwards:And ? - 4 cannot be zero, so x cannot be 4: So all together we end up with:B. [1, 4)? 4,833.Let ? ? =? + 1. Which of the following is true? Explain your answer.3. D_ A. fis an even function. B. fis an odd function. C. fis both even and odd. D. fis neither even nor odd. Solution: When ? -? = ? ? then the function is even.When ? -?=-? ? then the function is odd.3 3? -? = (-? ) + 1 =-(? ) + 1is not equal to ? ? or -? ?Therefore the function is neither even nor odd. 4. The time it takes to clean up after a party varies inversely with the number of people workingon the job. If 4 people could complete the clean-up in 35 minutes, then how long (to the nearestminute) would it take for 7 people? Show work.4. _B_____A.16 minutesB. 20 minutesC. 32 minutesD.61 minutesLet the total area to be cleaned be? , Given that it takes 35 minutes for each person toclean an area of ? /4.Therefore the total area to be cleaned is equal to ? = 35* 4 = 140140 The time taken by 7 people to clean the same will be = 20 minutes7 5. Suppose a gardener has 40 yards of fencing to make a rectangular garden enclosure. If theenclosure is x yards long, express the area A of the enclosure as a function of the length x.Briefly explain your choice (You may find it helpful to draw a picture, but it is not necessary to submit it.)5. __A____ 2A.A(x) = 20x – x2B. A(x) = 40x – x2C.A(x) = x – 40x2 D.A(x) =1600-?Let length of the rectangular fencing be x. Given total length of the fencing = 40 yards.Therefore the breath is equal to 20 – xyards.2 Area is equal to A(x) = length X breath = (20 – x) X x=20x – x 6.For each graph, is the graph symmetric with respect to the x-axis? y-axis? origin?(Noexplanation required. Just answer Yes or No to each question.)(a) (b) (c) Symmetric with respect to the Symmetric with respect toSymmetric with respect to the thex-axis? _N_x-axis? _N_x-axis? _Y_y-axis? _Y_ y-axis? _N_ y-axis? _N_ origin? _N_ origin? _N__origin? _N_7.A graph of y = f (x) follows. No formula for fis given.7. ____C___ Which graph (A, B, C, or D) represents the graph of =? ? - 1 - 2?BRIEFLY EXPLAIN how you have decided which graph is the correct one.y = f(x) (below) (Grid supplied for scratch work; You are NOT required to submit your own graph) 44222 4-4 -22 4-4 -2-2-2-4-4 A. B.4 4222 4-4 -2-4 -2 2 4-2-2-4-4 C. D.4 42 2-2 2 4 -2 2 4-4 -4-2 -2-4 -4 Explain why I choice C y =f(x) y X equal to? ? - 1 Y equal to? - 2 x y (1) (2) (3) -3 -2 -2 -3=x-1? -2 -2-2 =-4 (-2,-4)-2 -2 -2 -2=x-1 ? -1 -2-2=-4 (-1,-4)-1 0 0 -1=x-1 ? 0 0-2=-2 (0,-2)0 2 2 0=x-1 ? 1 2-2=0 (1,0)2 2 2 2=x-1 ? 3 2-2=0 (3,0)y = f(x) (below) 8. no explanation required) Consider the graph of the piecewise function y = f (x) pictured below. (a) State the value of f ( -2).Ans: 2(b) State the domain of the piecewise function.Ans: ( -6, -4, 0, 3, 4)(c) State the range of the piecewise function.Ans: ( -2, 0, 1, 2 )(d) State the interval(s) on which the function is increasing. That is, for what x-values isthe function increasing?Ans: ( -6, -4 ) and ( 3, 4 )(e) State the interval(s) on which the function is decreasing. That is, for what x-values isthe function decreasing? Ans: ( 0, 3 )(f) The piecewise function has many pieces. Write the formula for just ONE PIECE ofthis piecewise function. (You choose the piece you prefer. No explanation required)f(x) = _2_for _domain (-4, 0)_____ (state the x-values associated with your piece).2 9. Letf(x) = 2x – 5x+1 andg(x) = 1 – x.(a) Find the difference (f– g)(x) and simplify the results. Show work.We write two functions according to the subtraction operation. 2 (f– g)(x) = (2x – 5x + 1) – (1 – x)2 2 (f– g)(x) =2x – 5x + 1–1+x =2x – 4x(f–g)(x)=2x(x –2)(b) Find (f– g)(–1) and simplify the results. Show work.(f–g)(x)= 2x(x –2)Substitute the value of x with -1(f–g)(–1) = 2*(-1)((-1) –2)=6(c) Findthe composite function? ? ??and simplify the results. Show work.To perform this composition, we introduce the function g as variable of the function f2? ? ? = 2? ? - 5 ? ? + 12 Where g(x) = 1 – x andf (x) = 2x – 5x + 1We group the variables and constants2 (f ? g)(x) =21 – ? - 5 1 – ? + 12(f ? g)(x)=2 x - 2? + 1 - 5 + 5? + 12(f ? g)(x)= 2x - 4? + 2 - 5 + 5? + 12 (f ? g)(x)=2x +? - 2(d) Find? ? ?3 . Show some work.2 (f ? g)(x)=2x +? - 2Substitute the value of x with 32 (f ? g)(3)=2* 3 + 3- 2 = 19 "