Write the restrictions that should be imposed on the variable for each of the following function. Then find, explicitly, the domain for each function. Write the answer using interval notation. a) f (x ) = 2x2 -x+1 x -5 b ) g ( p ) = 1 4 - 2p Q4. Average rate of change The average rate of change of a function f from x, to X2 is (*2)-f(x1). Given the function f (x) = -8x + 5, determine the average rate of change from x = -1 to x = 5 *2 - x1 Q5. Graphing a Piecewise Function about the isaxis and Graph the function f (x) = 3x + 1 for x S 1 1-2 for x > 1 //BNBagel are also worth in the graphs of the Q6. Graphs of Basic Functions (https://goo.gl/DKFxvy) Match each graph with the name of the function: A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute Value function H. Cube root functionPRE-CLASS ASSIGNMENT Sections 2.6, 3.2, 3.3 Name: Print and complete this assignment. This assignment must be submitted on Canvas. Late submissions will not be accepted. It is essential you do this assignment so you can participate and understand the in-class group activities. You can use your textbook, internet, LAs, teamwork, etc.; however, copying another student's work will be considered cheating and dealt with accordingly. Q1. Operations on Functions - Video (https://goo.gl/8Uqi3R) In many problem-solving contexts, we will need to add, subtract, and multiply the two original functions together. Addition: (f + g)(x) = f(x)+g(x) Subtraction: (f - g)(x) = f(x) - g(x) Multiplication: (f . g)(x) = f(x) . g(x) Division: (f/g)(x) = f(x)/g(x) where g(x) # 0 Let f(x) = = and g(x) = *-1 x - 5 a. Find and simplify the formula for the function f + g. The domain of a new function combination are all input values that are in the domains of both original functions f and g. In the case of the domain of f/g we must remember not to divide by zero so we add a further restriction that g(x) cannot equal to zero. tion, identity b. Find the domain of the function f +g from part a. Q2. Video: Composition of two functions; Video: Forming a compositionTables for the functions f and g are given evaluate the expression if possible X -5 0 f ( x ) 0 5 10 5 10 - 5 X -5 5 10 15 g(x) 15 10 - 5 0 a. (gof)(0) b. (fog) (5) c. (gog) (10) Q3. Video: Evaluating composite function using graphs (https://goo.gl/cALsNd) Use the graphs of f and g to answer the questions a) Find following values (i) (f + 9 ) (- 2) (ii) (9 - f) (-3) (iii) (f g) (3) ( iv ) ( # ) (0) ( v) (fog ) (1) ( vi) (8.8 )-1) : Q4. Video: Definition of a polynomial ; Video: Polynomial functions Determine which of the following is a polynomial function. If it is a polynomial function, identify its degree, the leading term and the leading coefficient. If it is not a polynomial function, explain why not. a) f(x) = - 4x4vx +x2-5x+17 b) f(x)= 3+ x-7 c ) f ( x ) = V2 x5 - 7x2 - 8x Q5. Explore the graphs of polynomial functions by graphing some of them. Go toins: /www.desmos.com and enter an equation of a polynomial (for example enter y = -3x4 + 2X howzx+4 ). Draw different polynomials with different degrees. Zoom in and zoom out to see the graphs up-close and from a distance. a ) Did your graphs have breaks? h) Did your graphs have corners (sharp turns, as the absolute value function, for example)? Which of the graphs below could be a graph(s) of polynomial functions? Explain Q6. Video: Long division (https://goo.gl/75rp42) a) Write below the relationship between the dividend, divisor, quotient and remainder in the division process dividend = b) Use long division process to divide 2x5 - 8x4 + 2x3 + x2 by 2x3+ 1 Identify the following: Divisor: Dividend : Remainder: Quotient: Use the results to complete the statement below 2x5 - 8x4 + 2x3 + x2 = (2x3 + 1)( + c) Compare the degree of the divisor and the remainder. What do you notice? Generalize your observation by completing the statement belowThe degree of the remainder is always than the degree of the divisor. Q7. Video: Synthetic division (https://goo.gl/F2JHdz) ; Video: More examples of synthetic division (https://goo.gl/zG2BXE) a) Use synthetic division to divide 6x5 - 2x3 + 4x2 - 3x + 1 by x-2 b) Identify the quotient and the remainder Quotient: Remainder: c) Write your result in the form: dividend = divisor . quotient + remainder